topology.nhds_set | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

f2ce6086

(last sync)

chore(*): rename locale topological_space to topology (#18293)

Diff

@@ -24,7 +24,7 @@ Furthermore, we have the following results:
 -/
 
 open set filter
-open_locale topological_space filter
+open_locale topology filter
 
 variables {α β : Type*} [topological_space α] [topological_space β]
   {s t s₁ s₂ t₁ t₂ : set α} {x : α}
@@ -33,7 +33,7 @@ variables {α β : Type*} [topological_space α] [topological_space β]
 def nhds_set (s : set α) : filter α :=
 Sup (nhds '' s)
 
-localized "notation (name := nhds_set) `𝓝ˢ` := nhds_set" in topological_space
+localized "notation (name := nhds_set) `𝓝ˢ` := nhds_set" in topology
 
 lemma nhds_set_diagonal (α) [topological_space (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) :=
 by { rw [nhds_set, ← range_diag, ← range_comp], refl }

f7fc89d5

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

fac36901

bump to nightly-2024-04-25-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

ad7a2212

Diff

@@ -77,7 +77,7 @@ theorem mem_nhdsSet_iff_exists : s ∈ 𝓝ˢ t ↔ ∃ U : Set α, IsOpen U ∧
 
 #print hasBasis_nhdsSet /-
 theorem hasBasis_nhdsSet (s : Set α) : (𝓝ˢ s).HasBasis (fun U => IsOpen U ∧ s ⊆ U) fun U => U :=
-  ⟨fun t => by simp [mem_nhdsSet_iff_exists, and_assoc']⟩
+  ⟨fun t => by simp [mem_nhdsSet_iff_exists, and_assoc]⟩
 #align has_basis_nhds_set hasBasis_nhdsSet
 -/

fac36901

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Patrick Massot
 -/
-import Topology.Basic
+import Topology.Defs.Basic
 
 #align_import topology.nhds_set from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"

fac36901

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Patrick Massot
 -/
-import Mathbin.Topology.Basic
+import Topology.Basic
 
 #align_import topology.nhds_set from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"

fac36901

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -101,7 +101,7 @@ theorem nhdsSet_eq_principal_iff : 𝓝ˢ s = 𝓟 s ↔ IsOpen s := by
 #align nhds_set_eq_principal_iff nhdsSet_eq_principal_iff
 -/
 
-alias nhdsSet_eq_principal_iff ↔ _ IsOpen.nhdsSet_eq
+alias ⟨_, IsOpen.nhdsSet_eq⟩ := nhdsSet_eq_principal_iff
 #align is_open.nhds_set_eq IsOpen.nhdsSet_eq
 
 #print nhdsSet_interior /-

fac36901

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.nhds_set
-! leanprover-community/mathlib commit fac369018417f980cec5fcdafc766a69f88d8cfe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Basic
 
+#align_import topology.nhds_set from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"
+
 /-!
 # Neighborhoods of a set

fac36901

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -46,12 +46,13 @@ def nhdsSet (s : Set α) : Filter α :=
 #align nhds_set nhdsSet
 -/
 
--- mathport name: nhds_set
 scoped[Topology] notation "𝓝ˢ" => nhdsSet
 
+#print nhdsSet_diagonal /-
 theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) := by
   rw [nhdsSet, ← range_diag, ← range_comp]; rfl
 #align nhds_set_diagonal nhdsSet_diagonal
+-/
 
 #print mem_nhdsSet_iff_forall /-
 theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : α, x ∈ t → s ∈ 𝓝 x := by
@@ -89,9 +90,11 @@ theorem IsOpen.mem_nhdsSet (hU : IsOpen s) : s ∈ 𝓝ˢ t ↔ t ⊆ s := by
 #align is_open.mem_nhds_set IsOpen.mem_nhdsSet
 -/
 
+#print principal_le_nhdsSet /-
 theorem principal_le_nhdsSet : 𝓟 s ≤ 𝓝ˢ s := fun s hs =>
   (subset_interior_iff_mem_nhdsSet.mpr hs).trans interior_subset
 #align principal_le_nhds_set principal_le_nhdsSet
+-/
 
 #print nhdsSet_eq_principal_iff /-
 @[simp]
@@ -125,39 +128,53 @@ theorem mem_nhdsSet_interior : s ∈ 𝓝ˢ (interior s) :=
 #align mem_nhds_set_interior mem_nhdsSet_interior
 -/
 
+#print nhdsSet_empty /-
 @[simp]
 theorem nhdsSet_empty : 𝓝ˢ (∅ : Set α) = ⊥ := by rw [is_open_empty.nhds_set_eq, principal_empty]
 #align nhds_set_empty nhdsSet_empty
+-/
 
 #print mem_nhdsSet_empty /-
 theorem mem_nhdsSet_empty : s ∈ 𝓝ˢ (∅ : Set α) := by simp
 #align mem_nhds_set_empty mem_nhdsSet_empty
 -/
 
+#print nhdsSet_univ /-
 @[simp]
 theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [is_open_univ.nhds_set_eq, principal_univ]
 #align nhds_set_univ nhdsSet_univ
+-/
 
+#print nhdsSet_mono /-
 @[mono]
 theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
   sSup_le_sSup <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono
+-/
 
+#print monotone_nhdsSet /-
 theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set α → Filter α) := fun s t => nhdsSet_mono
 #align monotone_nhds_set monotone_nhdsSet
+-/
 
+#print nhds_le_nhdsSet /-
 theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
   le_sSup <| mem_image_of_mem _ h
 #align nhds_le_nhds_set nhds_le_nhdsSet
+-/
 
+#print nhdsSet_union /-
 @[simp]
 theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
   simp only [nhdsSet, image_union, sSup_union]
 #align nhds_set_union nhdsSet_union
+-/
 
+#print union_mem_nhdsSet /-
 theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ t₂) : s₁ ∪ s₂ ∈ 𝓝ˢ (t₁ ∪ t₂) := by
   rw [nhdsSet_union]; exact union_mem_sup h₁ h₂
 #align union_mem_nhds_set union_mem_nhdsSet
+-/
 
 #print Continuous.tendsto_nhdsSet /-
 /-- Preimage of a set neighborhood of `t` under a continuous map `f` is a set neighborhood of `s`

fac36901

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -35,7 +35,7 @@ Furthermore, we have the following results:
 
 open Set Filter
 
-open Topology Filter
+open scoped Topology Filter
 
 variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β] {s t s₁ s₂ t₁ t₂ : Set α} {x : α}

fac36901

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -49,12 +49,6 @@ def nhdsSet (s : Set α) : Filter α :=
 -- mathport name: nhds_set
 scoped[Topology] notation "𝓝ˢ" => nhdsSet
 
-/- warning: nhds_set_diagonal -> nhdsSet_diagonal is a dubious translation:
-lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
-but is expected to have type
-  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
-Case conversion may be inaccurate. Consider using '#align nhds_set_diagonal nhdsSet_diagonalₓ'. -/
 theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) := by
   rw [nhdsSet, ← range_diag, ← range_comp]; rfl
 #align nhds_set_diagonal nhdsSet_diagonal
@@ -95,12 +89,6 @@ theorem IsOpen.mem_nhdsSet (hU : IsOpen s) : s ∈ 𝓝ˢ t ↔ t ⊆ s := by
 #align is_open.mem_nhds_set IsOpen.mem_nhdsSet
 -/
 
-/- warning: principal_le_nhds_set -> principal_le_nhdsSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α}, LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α s) (nhdsSet.{u1} α _inst_1 s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α}, LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Filter.principal.{u1} α s) (nhdsSet.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align principal_le_nhds_set principal_le_nhdsSetₓ'. -/
 theorem principal_le_nhdsSet : 𝓟 s ≤ 𝓝ˢ s := fun s hs =>
   (subset_interior_iff_mem_nhdsSet.mpr hs).trans interior_subset
 #align principal_le_nhds_set principal_le_nhdsSet
@@ -137,12 +125,6 @@ theorem mem_nhdsSet_interior : s ∈ 𝓝ˢ (interior s) :=
 #align mem_nhds_set_interior mem_nhdsSet_interior
 -/
 
-/- warning: nhds_set_empty -> nhdsSet_empty is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
-Case conversion may be inaccurate. Consider using '#align nhds_set_empty nhdsSet_emptyₓ'. -/
 @[simp]
 theorem nhdsSet_empty : 𝓝ˢ (∅ : Set α) = ⊥ := by rw [is_open_empty.nhds_set_eq, principal_empty]
 #align nhds_set_empty nhdsSet_empty
@@ -152,63 +134,27 @@ theorem mem_nhdsSet_empty : s ∈ 𝓝ˢ (∅ : Set α) := by simp
 #align mem_nhds_set_empty mem_nhdsSet_empty
 -/
 
-/- warning: nhds_set_univ -> nhdsSet_univ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Set.univ.{u1} α)) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Set.univ.{u1} α)) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))
-Case conversion may be inaccurate. Consider using '#align nhds_set_univ nhdsSet_univₓ'. -/
 @[simp]
 theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [is_open_univ.nhds_set_eq, principal_univ]
 #align nhds_set_univ nhdsSet_univ
 
-/- warning: nhds_set_mono -> nhdsSet_mono is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
-Case conversion may be inaccurate. Consider using '#align nhds_set_mono nhdsSet_monoₓ'. -/
 @[mono]
 theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
   sSup_le_sSup <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono
 
-/- warning: monotone_nhds_set -> monotone_nhdsSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Monotone.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α)) (nhdsSet.{u1} α _inst_1)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Monotone.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α)) (nhdsSet.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align monotone_nhds_set monotone_nhdsSetₓ'. -/
 theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set α → Filter α) := fun s t => nhdsSet_mono
 #align monotone_nhds_set monotone_nhdsSet
 
-/- warning: nhds_le_nhds_set -> nhds_le_nhdsSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
-Case conversion may be inaccurate. Consider using '#align nhds_le_nhds_set nhds_le_nhdsSetₓ'. -/
 theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
   le_sSup <| mem_image_of_mem _ h
 #align nhds_le_nhds_set nhds_le_nhdsSet
 
-/- warning: nhds_set_union -> nhdsSet_union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
-Case conversion may be inaccurate. Consider using '#align nhds_set_union nhdsSet_unionₓ'. -/
 @[simp]
 theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
   simp only [nhdsSet, image_union, sSup_union]
 #align nhds_set_union nhdsSet_union
 
-/- warning: union_mem_nhds_set -> union_mem_nhdsSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s₁ : Set.{u1} α} {s₂ : Set.{u1} α} {t₁ : Set.{u1} α} {t₂ : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s₁ (nhdsSet.{u1} α _inst_1 t₁)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s₂ (nhdsSet.{u1} α _inst_1 t₂)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₂) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) t₁ t₂)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s₁ : Set.{u1} α} {s₂ : Set.{u1} α} {t₁ : Set.{u1} α} {t₂ : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s₁ (nhdsSet.{u1} α _inst_1 t₁)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s₂ (nhdsSet.{u1} α _inst_1 t₂)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s₁ s₂) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) t₁ t₂)))
-Case conversion may be inaccurate. Consider using '#align union_mem_nhds_set union_mem_nhdsSetₓ'. -/
 theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ t₂) : s₁ ∪ s₂ ∈ 𝓝ˢ (t₁ ∪ t₂) := by
   rw [nhdsSet_union]; exact union_mem_sup h₁ h₂
 #align union_mem_nhds_set union_mem_nhdsSet

fac36901

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -55,10 +55,8 @@ lean 3 declaration is
 but is expected to have type
   forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
 Case conversion may be inaccurate. Consider using '#align nhds_set_diagonal nhdsSet_diagonalₓ'. -/
-theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) :=
-  by
-  rw [nhdsSet, ← range_diag, ← range_comp]
-  rfl
+theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) := by
+  rw [nhdsSet, ← range_diag, ← range_comp]; rfl
 #align nhds_set_diagonal nhdsSet_diagonal
 
 #print mem_nhdsSet_iff_forall /-
@@ -211,10 +209,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s₁ : Set.{u1} α} {s₂ : Set.{u1} α} {t₁ : Set.{u1} α} {t₂ : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s₁ (nhdsSet.{u1} α _inst_1 t₁)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s₂ (nhdsSet.{u1} α _inst_1 t₂)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s₁ s₂) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) t₁ t₂)))
 Case conversion may be inaccurate. Consider using '#align union_mem_nhds_set union_mem_nhdsSetₓ'. -/
-theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ t₂) : s₁ ∪ s₂ ∈ 𝓝ˢ (t₁ ∪ t₂) :=
-  by
-  rw [nhdsSet_union]
-  exact union_mem_sup h₁ h₂
+theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ t₂) : s₁ ∪ s₂ ∈ 𝓝ˢ (t₁ ∪ t₂) := by
+  rw [nhdsSet_union]; exact union_mem_sup h₁ h₂
 #align union_mem_nhds_set union_mem_nhdsSet
 
 #print Continuous.tendsto_nhdsSet /-

fac36901

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -99,7 +99,7 @@ theorem IsOpen.mem_nhdsSet (hU : IsOpen s) : s ∈ 𝓝ˢ t ↔ t ⊆ s := by
 
 /- warning: principal_le_nhds_set -> principal_le_nhdsSet is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α}, LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α s) (nhdsSet.{u1} α _inst_1 s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α}, LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α s) (nhdsSet.{u1} α _inst_1 s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α}, LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Filter.principal.{u1} α s) (nhdsSet.{u1} α _inst_1 s)
 Case conversion may be inaccurate. Consider using '#align principal_le_nhds_set principal_le_nhdsSetₓ'. -/
@@ -166,7 +166,7 @@ theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [is_open_univ.nhds_
 
 /- warning: nhds_set_mono -> nhdsSet_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align nhds_set_mono nhdsSet_monoₓ'. -/
@@ -186,7 +186,7 @@ theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set α → Filter α) := fun s t =
 
 /- warning: nhds_le_nhds_set -> nhds_le_nhdsSet is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align nhds_le_nhds_set nhds_le_nhdsSetₓ'. -/

fac36901

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -42,7 +42,7 @@ variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β] {s t s₁
 #print nhdsSet /-
 /-- The filter of neighborhoods of a set in a topological space. -/
 def nhdsSet (s : Set α) : Filter α :=
-  supₛ (nhds '' s)
+  sSup (nhds '' s)
 #align nhds_set nhdsSet
 -/
 
@@ -51,9 +51,9 @@ scoped[Topology] notation "𝓝ˢ" => nhdsSet
 
 /- warning: nhds_set_diagonal -> nhdsSet_diagonal is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
+  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
 but is expected to have type
-  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
+  forall (α : Type.{u1}) [_inst_3 : TopologicalSpace.{u1} (Prod.{u1, u1} α α)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) _inst_3 (Set.diagonal.{u1} α)) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) _inst_3 (Prod.mk.{u1, u1} α α x x)))
 Case conversion may be inaccurate. Consider using '#align nhds_set_diagonal nhdsSet_diagonalₓ'. -/
 theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal α) = ⨆ x, 𝓝 (x, x) :=
   by
@@ -63,13 +63,13 @@ theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] : 𝓝ˢ (diagonal 
 
 #print mem_nhdsSet_iff_forall /-
 theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : α, x ∈ t → s ∈ 𝓝 x := by
-  simp_rw [nhdsSet, Filter.mem_supₛ, ball_image_iff]
+  simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]
 #align mem_nhds_set_iff_forall mem_nhdsSet_iff_forall
 -/
 
 #print bUnion_mem_nhdsSet /-
 theorem bUnion_mem_nhdsSet {t : α → Set α} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
-  mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) (subset_unionᵢ₂ x hx)
+  mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) (subset_iUnion₂ x hx)
 #align bUnion_mem_nhds_set bUnion_mem_nhdsSet
 -/
 
@@ -172,7 +172,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align nhds_set_mono nhdsSet_monoₓ'. -/
 @[mono]
 theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
-  supₛ_le_supₛ <| image_subset _ h
+  sSup_le_sSup <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono
 
 /- warning: monotone_nhds_set -> monotone_nhdsSet is a dubious translation:
@@ -191,7 +191,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (nhds.{u1} α _inst_1 x) (nhdsSet.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align nhds_le_nhds_set nhds_le_nhdsSetₓ'. -/
 theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
-  le_supₛ <| mem_image_of_mem _ h
+  le_sSup <| mem_image_of_mem _ h
 #align nhds_le_nhds_set nhds_le_nhdsSet
 
 /- warning: nhds_set_union -> nhdsSet_union is a dubious translation:
@@ -202,7 +202,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align nhds_set_union nhdsSet_unionₓ'. -/
 @[simp]
 theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
-  simp only [nhdsSet, image_union, supₛ_union]
+  simp only [nhdsSet, image_union, sSup_union]
 #align nhds_set_union nhdsSet_union
 
 /- warning: union_mem_nhds_set -> union_mem_nhdsSet is a dubious translation:

fac36901

bump to nightly-2023-02-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

2097f8af

Diff

@@ -196,9 +196,9 @@ theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
 
 /- warning: nhds_set_union -> nhdsSet_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasSup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasSup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Filter.{u1} α) (nhdsSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) (nhdsSet.{u1} α _inst_1 s) (nhdsSet.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align nhds_set_union nhdsSet_unionₓ'. -/
 @[simp]
 theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by

fac36901

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -39,7 +39,7 @@ theorem nhdsSet_diagonal (X) [TopologicalSpace (X × X)] :
 #align nhds_set_diagonal nhdsSet_diagonal
 
 theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : X, x ∈ t → s ∈ 𝓝 x := by
-  simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]
+  simp_rw [nhdsSet, Filter.mem_sSup, forall_mem_image]
 #align mem_nhds_set_iff_forall mem_nhdsSet_iff_forall
 
 lemma nhdsSet_le : 𝓝ˢ s ≤ f ↔ ∀ x ∈ s, 𝓝 x ≤ f := by simp [nhdsSet]

f2ce6086

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -46,7 +46,7 @@ lemma nhdsSet_le : 𝓝ˢ s ≤ f ↔ ∀ x ∈ s, 𝓝 x ≤ f := by simp [nhds
 
 theorem bUnion_mem_nhdsSet {t : X → Set X} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
   mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) <|
-    subset_iUnion₂ (s := fun x _ => t x) x hx -- porting note: fails to find `s`
+    subset_iUnion₂ (s := fun x _ => t x) x hx -- Porting note: fails to find `s`
 #align bUnion_mem_nhds_set bUnion_mem_nhdsSet
 
 theorem subset_interior_iff_mem_nhdsSet : s ⊆ interior t ↔ t ∈ 𝓝ˢ s := by

f2ce6086

chore(Topology): move some definitions to new files (#10151)

In some cases, the order of implicit arguments changed because now they appear in a different order in variables.

Also, some definitions used greek letters for topological spaces, changed to X/Y.

2e5d90d5

Diff

@@ -32,13 +32,6 @@ open Set Filter Topology
 variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {f : Filter X}
   {s t s₁ s₂ t₁ t₂ : Set X} {x : X}
 
-/-- The filter of neighborhoods of a set in a topological space. -/
-def nhdsSet (s : Set X) : Filter X :=
-  sSup (nhds '' s)
-#align nhds_set nhdsSet
-
-@[inherit_doc] scoped[Topology] notation "𝓝ˢ" => nhdsSet
-
 theorem nhdsSet_diagonal (X) [TopologicalSpace (X × X)] :
     𝓝ˢ (diagonal X) = ⨆ (x : X), 𝓝 (x, x) := by
   rw [nhdsSet, ← range_diag, ← range_comp]

f2ce6086

feat(Topology): add lift'_nhds_interior etc (#10175)

0311bbc2

Diff

@@ -86,6 +86,14 @@ theorem hasBasis_nhdsSet (s : Set X) : (𝓝ˢ s).HasBasis (fun U => IsOpen U 
   ⟨fun t => by simp [mem_nhdsSet_iff_exists, and_assoc]⟩
 #align has_basis_nhds_set hasBasis_nhdsSet
 
+@[simp]
+lemma lift'_nhdsSet_interior (s : Set X) : (𝓝ˢ s).lift' interior = 𝓝ˢ s :=
+  (hasBasis_nhdsSet s).lift'_interior_eq_self fun _ ↦ And.left
+
+lemma Filter.HasBasis.nhdsSet_interior {ι : Sort*} {p : ι → Prop} {s : ι → Set X} {t : Set X}
+    (h : (𝓝ˢ t).HasBasis p s) : (𝓝ˢ t).HasBasis p (interior <| s ·) :=
+  lift'_nhdsSet_interior t ▸ h.lift'_interior
+
 theorem IsOpen.mem_nhdsSet (hU : IsOpen s) : s ∈ 𝓝ˢ t ↔ t ⊆ s := by
   rw [← subset_interior_iff_mem_nhdsSet, hU.interior_eq]
 #align is_open.mem_nhds_set IsOpen.mem_nhdsSet

f2ce6086

feat: lemmas about NhdsSet (#9674)

From sphere-eversion; I'm just submitting these. Thanks to @urkud for some review suggestions.

b52b6c43

Diff

@@ -177,3 +177,45 @@ lemma Continuous.tendsto_nhdsSet_nhds
     Tendsto f (𝓝ˢ s) (𝓝 y) := by
   rw [← nhdsSet_singleton]
   exact h.tendsto_nhdsSet h'
+
+/- This inequality cannot be improved to an equality. For instance,
+if `X` has two elements and the coarse topology and `s` and `t` are distinct singletons then
+`𝓝ˢ (s ∩ t) = ⊥` while `𝓝ˢ s ⊓ 𝓝ˢ t = ⊤` and those are different. -/
+theorem nhdsSet_inter_le (s t : Set X) : 𝓝ˢ (s ∩ t) ≤ 𝓝ˢ s ⊓ 𝓝ˢ t :=
+  (monotone_nhdsSet (X := X)).map_inf_le s t
+
+variable (s) in
+theorem IsClosed.nhdsSet_le_sup (h : IsClosed t) : 𝓝ˢ s ≤ 𝓝ˢ (s ∩ t) ⊔ 𝓟 (tᶜ) :=
+  calc
+    𝓝ˢ s = 𝓝ˢ (s ∩ t ∪ s ∩ tᶜ) := by rw [Set.inter_union_compl s t]
+    _ = 𝓝ˢ (s ∩ t) ⊔ 𝓝ˢ (s ∩ tᶜ) := by rw [nhdsSet_union]
+    _ ≤ 𝓝ˢ (s ∩ t) ⊔ 𝓝ˢ (tᶜ) := (sup_le_sup_left (monotone_nhdsSet (s.inter_subset_right (tᶜ))) _)
+    _ = 𝓝ˢ (s ∩ t) ⊔ 𝓟 (tᶜ) := by rw [h.isOpen_compl.nhdsSet_eq]
+
+variable (s) in
+theorem IsClosed.nhdsSet_le_sup' (h : IsClosed t) :
+    𝓝ˢ s ≤ 𝓝ˢ (t ∩ s) ⊔ 𝓟 (tᶜ) := by rw [Set.inter_comm]; exact h.nhdsSet_le_sup s
+
+theorem Filter.Eventually.eventually_nhdsSet {p : X → Prop} (h : ∀ᶠ y in 𝓝ˢ s, p y) :
+    ∀ᶠ y in 𝓝ˢ s, ∀ᶠ x in 𝓝 y, p x :=
+  eventually_nhdsSet_iff_forall.mpr fun x x_in ↦
+    (eventually_nhdsSet_iff_forall.mp h x x_in).eventually_nhds
+
+theorem Filter.Eventually.union_nhdsSet {p : X → Prop} :
+    (∀ᶠ x in 𝓝ˢ (s ∪ t), p x) ↔ (∀ᶠ x in 𝓝ˢ s, p x) ∧ ∀ᶠ x in 𝓝ˢ t, p x := by
+  rw [nhdsSet_union, eventually_sup]
+
+theorem Filter.Eventually.union {p : X → Prop} (hs : ∀ᶠ x in 𝓝ˢ s, p x) (ht : ∀ᶠ x in 𝓝ˢ t, p x) :
+    ∀ᶠ x in 𝓝ˢ (s ∪ t), p x :=
+  Filter.Eventually.union_nhdsSet.mpr ⟨hs, ht⟩
+
+theorem nhdsSet_iUnion {ι : Sort*} (s : ι → Set X) : 𝓝ˢ (⋃ i, s i) = ⨆ i, 𝓝ˢ (s i) := by
+  simp only [nhdsSet, image_iUnion, sSup_iUnion (β := Filter X)]
+
+theorem eventually_nhdsSet_iUnion₂ {ι : Sort*} {p : ι → Prop} {s : ι → Set X} {P : X → Prop} :
+    (∀ᶠ x in 𝓝ˢ (⋃ (i) (_ : p i), s i), P x) ↔ ∀ i, p i → ∀ᶠ x in 𝓝ˢ (s i), P x := by
+  simp only [nhdsSet_iUnion, eventually_iSup]
+
+theorem eventually_nhdsSet_iUnion {ι : Sort*} {s : ι → Set X} {P : X → Prop} :
+    (∀ᶠ x in 𝓝ˢ (⋃ i, s i), P x) ↔ ∀ i, ∀ᶠ x in 𝓝ˢ (s i), P x := by
+  simp only [nhdsSet_iUnion, eventually_iSup]

f2ce6086

chore(Topology/NhdsSet): rename type variables (#9673)

Now we use letters X and Y for topological spaces, not Greek letters.

2a498095

Diff

@@ -17,8 +17,8 @@ In this file we define the filter `𝓝ˢ s` or `nhdsSet s` consisting of all ne
 
 There are a couple different notions equivalent to `s ∈ 𝓝ˢ t`:
 * `s ⊆ interior t` using `subset_interior_iff_mem_nhdsSet`
-* `∀ x : α, x ∈ t → s ∈ 𝓝 x` using `mem_nhdsSet_iff_forall`
-* `∃ U : Set α, IsOpen U ∧ t ⊆ U ∧ U ⊆ s` using `mem_nhdsSet_iff_exists`
+* `∀ x : X, x ∈ t → s ∈ 𝓝 x` using `mem_nhdsSet_iff_forall`
+* `∃ U : Set X, IsOpen U ∧ t ⊆ U ∧ U ⊆ s` using `mem_nhdsSet_iff_exists`
 
 Furthermore, we have the following results:
 * `monotone_nhdsSet`: `𝓝ˢ` is monotone
@@ -29,29 +29,29 @@ Furthermore, we have the following results:
 
 open Set Filter Topology
 
-variable {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] {f : Filter α}
-  {s t s₁ s₂ t₁ t₂ : Set α} {x : α}
+variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {f : Filter X}
+  {s t s₁ s₂ t₁ t₂ : Set X} {x : X}
 
 /-- The filter of neighborhoods of a set in a topological space. -/
-def nhdsSet (s : Set α) : Filter α :=
+def nhdsSet (s : Set X) : Filter X :=
   sSup (nhds '' s)
 #align nhds_set nhdsSet
 
 @[inherit_doc] scoped[Topology] notation "𝓝ˢ" => nhdsSet
 
-theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] :
-    𝓝ˢ (diagonal α) = ⨆ (x : α), 𝓝 (x, x) := by
+theorem nhdsSet_diagonal (X) [TopologicalSpace (X × X)] :
+    𝓝ˢ (diagonal X) = ⨆ (x : X), 𝓝 (x, x) := by
   rw [nhdsSet, ← range_diag, ← range_comp]
   rfl
 #align nhds_set_diagonal nhdsSet_diagonal
 
-theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : α, x ∈ t → s ∈ 𝓝 x := by
+theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : X, x ∈ t → s ∈ 𝓝 x := by
   simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]
 #align mem_nhds_set_iff_forall mem_nhdsSet_iff_forall
 
-lemma nhdsSet_le : 𝓝ˢ s ≤ f ↔ ∀ a ∈ s, 𝓝 a ≤ f := by simp [nhdsSet]
+lemma nhdsSet_le : 𝓝ˢ s ≤ f ↔ ∀ x ∈ s, 𝓝 x ≤ f := by simp [nhdsSet]
 
-theorem bUnion_mem_nhdsSet {t : α → Set α} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
+theorem bUnion_mem_nhdsSet {t : X → Set X} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
   mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) <|
     subset_iUnion₂ (s := fun x _ => t x) x hx -- porting note: fails to find `s`
 #align bUnion_mem_nhds_set bUnion_mem_nhdsSet
@@ -67,22 +67,22 @@ theorem disjoint_principal_nhdsSet : Disjoint (𝓟 s) (𝓝ˢ t) ↔ Disjoint (
 theorem disjoint_nhdsSet_principal : Disjoint (𝓝ˢ s) (𝓟 t) ↔ Disjoint s (closure t) := by
   rw [disjoint_comm, disjoint_principal_nhdsSet, disjoint_comm]
 
-theorem mem_nhdsSet_iff_exists : s ∈ 𝓝ˢ t ↔ ∃ U : Set α, IsOpen U ∧ t ⊆ U ∧ U ⊆ s := by
+theorem mem_nhdsSet_iff_exists : s ∈ 𝓝ˢ t ↔ ∃ U : Set X, IsOpen U ∧ t ⊆ U ∧ U ⊆ s := by
   rw [← subset_interior_iff_mem_nhdsSet, subset_interior_iff]
 #align mem_nhds_set_iff_exists mem_nhdsSet_iff_exists
 
 /-- A proposition is true on a set neighborhood of `s` iff it is true on a larger open set -/
-theorem eventually_nhdsSet_iff_exists {p : α → Prop} :
+theorem eventually_nhdsSet_iff_exists {p : X → Prop} :
     (∀ᶠ x in 𝓝ˢ s, p x) ↔ ∃ t, IsOpen t ∧ s ⊆ t ∧ ∀ x, x ∈ t → p x :=
   mem_nhdsSet_iff_exists
 
 /-- A proposition is true on a set neighborhood of `s`
 iff it is eventually true near each point in the set. -/
-theorem eventually_nhdsSet_iff_forall {p : α → Prop} :
+theorem eventually_nhdsSet_iff_forall {p : X → Prop} :
     (∀ᶠ x in 𝓝ˢ s, p x) ↔ ∀ x, x ∈ s → ∀ᶠ y in 𝓝 x, p y :=
   mem_nhdsSet_iff_forall
 
-theorem hasBasis_nhdsSet (s : Set α) : (𝓝ˢ s).HasBasis (fun U => IsOpen U ∧ s ⊆ U) fun U => U :=
+theorem hasBasis_nhdsSet (s : Set X) : (𝓝ˢ s).HasBasis (fun U => IsOpen U ∧ s ⊆ U) fun U => U :=
   ⟨fun t => by simp [mem_nhdsSet_iff_exists, and_assoc]⟩
 #align has_basis_nhds_set hasBasis_nhdsSet
 
@@ -99,10 +99,10 @@ theorem principal_le_nhdsSet : 𝓟 s ≤ 𝓝ˢ s := fun _s hs =>
 
 theorem subset_of_mem_nhdsSet (h : t ∈ 𝓝ˢ s) : s ⊆ t := principal_le_nhdsSet h
 
-theorem Filter.Eventually.self_of_nhdsSet {p : α → Prop} (h : ∀ᶠ x in 𝓝ˢ s, p x) : ∀ x ∈ s, p x :=
+theorem Filter.Eventually.self_of_nhdsSet {p : X → Prop} (h : ∀ᶠ x in 𝓝ˢ s, p x) : ∀ x ∈ s, p x :=
   principal_le_nhdsSet h
 
-nonrec theorem Filter.EventuallyEq.self_of_nhdsSet {f g : α → β} (h : f =ᶠ[𝓝ˢ s] g) : EqOn f g s :=
+nonrec theorem Filter.EventuallyEq.self_of_nhdsSet {f g : X → Y} (h : f =ᶠ[𝓝ˢ s] g) : EqOn f g s :=
   h.self_of_nhdsSet
 
 @[simp]
@@ -128,14 +128,14 @@ theorem mem_nhdsSet_interior : s ∈ 𝓝ˢ (interior s) :=
 #align mem_nhds_set_interior mem_nhdsSet_interior
 
 @[simp]
-theorem nhdsSet_empty : 𝓝ˢ (∅ : Set α) = ⊥ := by rw [isOpen_empty.nhdsSet_eq, principal_empty]
+theorem nhdsSet_empty : 𝓝ˢ (∅ : Set X) = ⊥ := by rw [isOpen_empty.nhdsSet_eq, principal_empty]
 #align nhds_set_empty nhdsSet_empty
 
-theorem mem_nhdsSet_empty : s ∈ 𝓝ˢ (∅ : Set α) := by simp
+theorem mem_nhdsSet_empty : s ∈ 𝓝ˢ (∅ : Set X) := by simp
 #align mem_nhds_set_empty mem_nhdsSet_empty
 
 @[simp]
-theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [isOpen_univ.nhdsSet_eq, principal_univ]
+theorem nhdsSet_univ : 𝓝ˢ (univ : Set X) = ⊤ := by rw [isOpen_univ.nhdsSet_eq, principal_univ]
 #align nhds_set_univ nhdsSet_univ
 
 @[mono]
@@ -143,7 +143,7 @@ theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
   sSup_le_sSup <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono
 
-theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set α → Filter α) := fun _ _ => nhdsSet_mono
+theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set X → Filter X) := fun _ _ => nhdsSet_mono
 #align monotone_nhds_set monotone_nhdsSet
 
 theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
@@ -151,7 +151,7 @@ theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
 #align nhds_le_nhds_set nhds_le_nhdsSet
 
 @[simp]
-theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
+theorem nhdsSet_union (s t : Set X) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
   simp only [nhdsSet, image_union, sSup_union]
 #align nhds_set_union nhdsSet_union
 
@@ -161,19 +161,19 @@ theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ
 #align union_mem_nhds_set union_mem_nhdsSet
 
 @[simp]
-theorem nhdsSet_insert (x : α) (s : Set α) : 𝓝ˢ (insert x s) = 𝓝 x ⊔ 𝓝ˢ s := by
+theorem nhdsSet_insert (x : X) (s : Set X) : 𝓝ˢ (insert x s) = 𝓝 x ⊔ 𝓝ˢ s := by
   rw [insert_eq, nhdsSet_union, nhdsSet_singleton]
 
 /-- Preimage of a set neighborhood of `t` under a continuous map `f` is a set neighborhood of `s`
 provided that `f` maps `s` to `t`.  -/
-theorem Continuous.tendsto_nhdsSet {f : α → β} {t : Set β} (hf : Continuous f)
+theorem Continuous.tendsto_nhdsSet {f : X → Y} {t : Set Y} (hf : Continuous f)
     (hst : MapsTo f s t) : Tendsto f (𝓝ˢ s) (𝓝ˢ t) :=
   ((hasBasis_nhdsSet s).tendsto_iff (hasBasis_nhdsSet t)).mpr fun U hU =>
     ⟨f ⁻¹' U, ⟨hU.1.preimage hf, hst.mono Subset.rfl hU.2⟩, fun _ => id⟩
 #align continuous.tendsto_nhds_set Continuous.tendsto_nhdsSet
 
-lemma Continuous.tendsto_nhdsSet_nhds {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
-    {s : Set X} {y : Y} {f : X → Y} (h : Continuous f) (h' : EqOn f (fun _ ↦ y) s) :
+lemma Continuous.tendsto_nhdsSet_nhds
+    {y : Y} {f : X → Y} (h : Continuous f) (h' : EqOn f (fun _ ↦ y) s) :
     Tendsto f (𝓝ˢ s) (𝓝 y) := by
   rw [← nhdsSet_singleton]
   exact h.tendsto_nhdsSet h'

f2ce6086

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -175,5 +175,5 @@ theorem Continuous.tendsto_nhdsSet {f : α → β} {t : Set β} (hf : Continuous
 lemma Continuous.tendsto_nhdsSet_nhds {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
     {s : Set X} {y : Y} {f : X → Y} (h : Continuous f) (h' : EqOn f (fun _ ↦ y) s) :
     Tendsto f (𝓝ˢ s) (𝓝 y) := by
-  rw [←nhdsSet_singleton]
+  rw [← nhdsSet_singleton]
   exact h.tendsto_nhdsSet h'

f2ce6086

feat(Topology/CompletelyRegular): Add definition CompletelyRegularSpace (#7926)

Add definitions CompletelyRegularSpace and T35Space.

23717cb8

Diff

@@ -171,3 +171,9 @@ theorem Continuous.tendsto_nhdsSet {f : α → β} {t : Set β} (hf : Continuous
   ((hasBasis_nhdsSet s).tendsto_iff (hasBasis_nhdsSet t)).mpr fun U hU =>
     ⟨f ⁻¹' U, ⟨hU.1.preimage hf, hst.mono Subset.rfl hU.2⟩, fun _ => id⟩
 #align continuous.tendsto_nhds_set Continuous.tendsto_nhdsSet
+
+lemma Continuous.tendsto_nhdsSet_nhds {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
+    {s : Set X} {y : Y} {f : X → Y} (h : Continuous f) (h' : EqOn f (fun _ ↦ y) s) :
+    Tendsto f (𝓝ˢ s) (𝓝 y) := by
+  rw [←nhdsSet_singleton]
+  exact h.tendsto_nhdsSet h'

f2ce6086

feat(NhdsSet): lemmas from the Mandelbrot set connectedness project (#7914)

Add eventually_nhdsSet_iff_exists, eventually_nhdsSet_iff_forall, and IsOpen.mem_nhdsSet_self.

Co-authored-by: @girving

c60a7805

Diff

@@ -71,6 +71,17 @@ theorem mem_nhdsSet_iff_exists : s ∈ 𝓝ˢ t ↔ ∃ U : Set α, IsOpen U ∧
   rw [← subset_interior_iff_mem_nhdsSet, subset_interior_iff]
 #align mem_nhds_set_iff_exists mem_nhdsSet_iff_exists
 
+/-- A proposition is true on a set neighborhood of `s` iff it is true on a larger open set -/
+theorem eventually_nhdsSet_iff_exists {p : α → Prop} :
+    (∀ᶠ x in 𝓝ˢ s, p x) ↔ ∃ t, IsOpen t ∧ s ⊆ t ∧ ∀ x, x ∈ t → p x :=
+  mem_nhdsSet_iff_exists
+
+/-- A proposition is true on a set neighborhood of `s`
+iff it is eventually true near each point in the set. -/
+theorem eventually_nhdsSet_iff_forall {p : α → Prop} :
+    (∀ᶠ x in 𝓝ˢ s, p x) ↔ ∀ x, x ∈ s → ∀ᶠ y in 𝓝 x, p y :=
+  mem_nhdsSet_iff_forall
+
 theorem hasBasis_nhdsSet (s : Set α) : (𝓝ˢ s).HasBasis (fun U => IsOpen U ∧ s ⊆ U) fun U => U :=
   ⟨fun t => by simp [mem_nhdsSet_iff_exists, and_assoc]⟩
 #align has_basis_nhds_set hasBasis_nhdsSet
@@ -79,6 +90,9 @@ theorem IsOpen.mem_nhdsSet (hU : IsOpen s) : s ∈ 𝓝ˢ t ↔ t ⊆ s := by
   rw [← subset_interior_iff_mem_nhdsSet, hU.interior_eq]
 #align is_open.mem_nhds_set IsOpen.mem_nhdsSet
 
+/-- An open set belongs to its own set neighborhoods filter. -/
+theorem IsOpen.mem_nhdsSet_self (ho : IsOpen s) : s ∈ 𝓝ˢ s := ho.mem_nhdsSet.mpr Subset.rfl
+
 theorem principal_le_nhdsSet : 𝓟 s ≤ 𝓝ˢ s := fun _s hs =>
   (subset_interior_iff_mem_nhdsSet.mpr hs).trans interior_subset
 #align principal_le_nhds_set principal_le_nhdsSet

f2ce6086

feat: Exterior of a set (#6982)

In an Alexandrov-discrete space, every set has a smallest neighborhood. We call this neighborhood the exterior of the set. It is completely analogous to the interior, except that all inclusions are reversed.

4bc2392b

Diff

@@ -29,7 +29,8 @@ Furthermore, we have the following results:
 
 open Set Filter Topology
 
-variable {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] {s t s₁ s₂ t₁ t₂ : Set α} {x : α}
+variable {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] {f : Filter α}
+  {s t s₁ s₂ t₁ t₂ : Set α} {x : α}
 
 /-- The filter of neighborhoods of a set in a topological space. -/
 def nhdsSet (s : Set α) : Filter α :=
@@ -48,6 +49,8 @@ theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : α, x ∈ t → s 
   simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]
 #align mem_nhds_set_iff_forall mem_nhdsSet_iff_forall
 
+lemma nhdsSet_le : 𝓝ˢ s ≤ f ↔ ∀ a ∈ s, 𝓝 a ≤ f := by simp [nhdsSet]
+
 theorem bUnion_mem_nhdsSet {t : α → Set α} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
   mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) <|
     subset_iUnion₂ (s := fun x _ => t x) x hx -- porting note: fails to find `s`

f2ce6086

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -94,7 +94,7 @@ theorem nhdsSet_eq_principal_iff : 𝓝ˢ s = 𝓟 s ↔ IsOpen s := by
     isOpen_iff_mem_nhds]
 #align nhds_set_eq_principal_iff nhdsSet_eq_principal_iff
 
-alias nhdsSet_eq_principal_iff ↔ _ IsOpen.nhdsSet_eq
+alias ⟨_, IsOpen.nhdsSet_eq⟩ := nhdsSet_eq_principal_iff
 #align is_open.nhds_set_eq IsOpen.nhdsSet_eq
 
 @[simp]

f2ce6086

feat: add Filter.Eventually.self_of_nhdsSet (#6497)

Also add subset_of_mem_nhdsSet. From the Sphere Eversion Project.

ec5f4d95

Diff

@@ -80,6 +80,14 @@ theorem principal_le_nhdsSet : 𝓟 s ≤ 𝓝ˢ s := fun _s hs =>
   (subset_interior_iff_mem_nhdsSet.mpr hs).trans interior_subset
 #align principal_le_nhds_set principal_le_nhdsSet
 
+theorem subset_of_mem_nhdsSet (h : t ∈ 𝓝ˢ s) : s ⊆ t := principal_le_nhdsSet h
+
+theorem Filter.Eventually.self_of_nhdsSet {p : α → Prop} (h : ∀ᶠ x in 𝓝ˢ s, p x) : ∀ x ∈ s, p x :=
+  principal_le_nhdsSet h
+
+nonrec theorem Filter.EventuallyEq.self_of_nhdsSet {f g : α → β} (h : f =ᶠ[𝓝ˢ s] g) : EqOn f g s :=
+  h.self_of_nhdsSet
+
 @[simp]
 theorem nhdsSet_eq_principal_iff : 𝓝ˢ s = 𝓟 s ↔ IsOpen s := by
   rw [← principal_le_nhdsSet.le_iff_eq, le_principal_iff, mem_nhdsSet_iff_forall,
@@ -95,9 +103,7 @@ theorem nhdsSet_interior : 𝓝ˢ (interior s) = 𝓟 (interior s) :=
 #align nhds_set_interior nhdsSet_interior
 
 @[simp]
-theorem nhdsSet_singleton : 𝓝ˢ {x} = 𝓝 x := by
-  ext
-  rw [← subset_interior_iff_mem_nhdsSet, ← mem_interior_iff_mem_nhds, singleton_subset_iff]
+theorem nhdsSet_singleton : 𝓝ˢ {x} = 𝓝 x := by simp [nhdsSet]
 #align nhds_set_singleton nhdsSet_singleton
 
 theorem mem_nhdsSet_interior : s ∈ 𝓝ˢ (interior s) :=

f2ce6086

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -29,7 +29,7 @@ Furthermore, we have the following results:
 
 open Set Filter Topology
 
-variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β] {s t s₁ s₂ t₁ t₂ : Set α} {x : α}
+variable {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] {s t s₁ s₂ t₁ t₂ : Set α} {x : α}
 
 /-- The filter of neighborhoods of a set in a topological space. -/
 def nhdsSet (s : Set α) : Filter α :=

f2ce6086

feat(Topology/Order/NhdsSet): new file (#6161)

Prove lemmas about neighborhoods of intervals.

Some lemmas are TC-generalizations of lemmas from the Sphere Eversion Project.

0938530e

Diff

@@ -137,6 +137,10 @@ theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ
   exact union_mem_sup h₁ h₂
 #align union_mem_nhds_set union_mem_nhdsSet
 
+@[simp]
+theorem nhdsSet_insert (x : α) (s : Set α) : 𝓝ˢ (insert x s) = 𝓝 x ⊔ 𝓝ˢ s := by
+  rw [insert_eq, nhdsSet_union, nhdsSet_singleton]
+
 /-- Preimage of a set neighborhood of `t` under a continuous map `f` is a set neighborhood of `s`
 provided that `f` maps `s` to `t`.  -/
 theorem Continuous.tendsto_nhdsSet {f : α → β} {t : Set β} (hf : Continuous f)

f2ce6086

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.nhds_set
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Basic
 
+#align_import topology.nhds_set from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Neighborhoods of a set

f2ce6086

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -36,7 +36,7 @@ variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β] {s t s₁
 
 /-- The filter of neighborhoods of a set in a topological space. -/
 def nhdsSet (s : Set α) : Filter α :=
-  supₛ (nhds '' s)
+  sSup (nhds '' s)
 #align nhds_set nhdsSet
 
 @[inherit_doc] scoped[Topology] notation "𝓝ˢ" => nhdsSet
@@ -48,12 +48,12 @@ theorem nhdsSet_diagonal (α) [TopologicalSpace (α × α)] :
 #align nhds_set_diagonal nhdsSet_diagonal
 
 theorem mem_nhdsSet_iff_forall : s ∈ 𝓝ˢ t ↔ ∀ x : α, x ∈ t → s ∈ 𝓝 x := by
-  simp_rw [nhdsSet, Filter.mem_supₛ, ball_image_iff]
+  simp_rw [nhdsSet, Filter.mem_sSup, ball_image_iff]
 #align mem_nhds_set_iff_forall mem_nhdsSet_iff_forall
 
 theorem bUnion_mem_nhdsSet {t : α → Set α} (h : ∀ x ∈ s, t x ∈ 𝓝 x) : (⋃ x ∈ s, t x) ∈ 𝓝ˢ s :=
   mem_nhdsSet_iff_forall.2 fun x hx => mem_of_superset (h x hx) <|
-    subset_unionᵢ₂ (s := fun x _ => t x) x hx -- porting note: fails to find `s`
+    subset_iUnion₂ (s := fun x _ => t x) x hx -- porting note: fails to find `s`
 #align bUnion_mem_nhds_set bUnion_mem_nhdsSet
 
 theorem subset_interior_iff_mem_nhdsSet : s ⊆ interior t ↔ t ∈ 𝓝ˢ s := by
@@ -120,19 +120,19 @@ theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [isOpen_univ.nhdsSe
 
 @[mono]
 theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
-  supₛ_le_supₛ <| image_subset _ h
+  sSup_le_sSup <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono
 
 theorem monotone_nhdsSet : Monotone (𝓝ˢ : Set α → Filter α) := fun _ _ => nhdsSet_mono
 #align monotone_nhds_set monotone_nhdsSet
 
 theorem nhds_le_nhdsSet (h : x ∈ s) : 𝓝 x ≤ 𝓝ˢ s :=
-  le_supₛ <| mem_image_of_mem _ h
+  le_sSup <| mem_image_of_mem _ h
 #align nhds_le_nhds_set nhds_le_nhdsSet
 
 @[simp]
 theorem nhdsSet_union (s t : Set α) : 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t := by
-  simp only [nhdsSet, image_union, supₛ_union]
+  simp only [nhdsSet, image_union, sSup_union]
 #align nhds_set_union nhdsSet_union
 
 theorem union_mem_nhdsSet (h₁ : s₁ ∈ 𝓝ˢ t₁) (h₂ : s₂ ∈ 𝓝ˢ t₂) : s₁ ∪ s₂ ∈ 𝓝ˢ (t₁ ∪ t₂) := by
@@ -147,4 +147,3 @@ theorem Continuous.tendsto_nhdsSet {f : α → β} {t : Set β} (hf : Continuous
   ((hasBasis_nhdsSet s).tendsto_iff (hasBasis_nhdsSet t)).mpr fun U hU =>
     ⟨f ⁻¹' U, ⟨hU.1.preimage hf, hst.mono Subset.rfl hU.2⟩, fun _ => id⟩
 #align continuous.tendsto_nhds_set Continuous.tendsto_nhdsSet
-

f2ce6086

feat: port Topology.Algebra.WithZeroTopology (#2703)

27f3e683

Diff

@@ -60,6 +60,13 @@ theorem subset_interior_iff_mem_nhdsSet : s ⊆ interior t ↔ t ∈ 𝓝ˢ s :=
   simp_rw [mem_nhdsSet_iff_forall, subset_interior_iff_nhds]
 #align subset_interior_iff_mem_nhds_set subset_interior_iff_mem_nhdsSet
 
+theorem disjoint_principal_nhdsSet : Disjoint (𝓟 s) (𝓝ˢ t) ↔ Disjoint (closure s) t := by
+  rw [disjoint_principal_left, ← subset_interior_iff_mem_nhdsSet, interior_compl,
+    subset_compl_iff_disjoint_left]
+
+theorem disjoint_nhdsSet_principal : Disjoint (𝓝ˢ s) (𝓟 t) ↔ Disjoint s (closure t) := by
+  rw [disjoint_comm, disjoint_principal_nhdsSet, disjoint_comm]
+
 theorem mem_nhdsSet_iff_exists : s ∈ 𝓝ˢ t ↔ ∃ U : Set α, IsOpen U ∧ t ⊆ U ∧ U ⊆ s := by
   rw [← subset_interior_iff_mem_nhdsSet, subset_interior_iff]
 #align mem_nhds_set_iff_exists mem_nhdsSet_iff_exists

f2ce6086

chore: Restore most of the mono attribute (#2491)

Restore most of the mono attribute now that #1740 is merged.

I think I got all of the monos.

ffb5ddde

Diff

@@ -111,7 +111,7 @@ theorem mem_nhdsSet_empty : s ∈ 𝓝ˢ (∅ : Set α) := by simp
 theorem nhdsSet_univ : 𝓝ˢ (univ : Set α) = ⊤ := by rw [isOpen_univ.nhdsSet_eq, principal_univ]
 #align nhds_set_univ nhdsSet_univ
 
--- porting note: todo: restore @[mono]
+@[mono]
 theorem nhdsSet_mono (h : s ⊆ t) : 𝓝ˢ s ≤ 𝓝ˢ t :=
   supₛ_le_supₛ <| image_subset _ h
 #align nhds_set_mono nhdsSet_mono

f2ce6086

chore: resync ported files (#2135)

This PR resyncs the first 28 entries of https://leanprover-community.github.io/mathlib-port-status/out-of-sync.html after sorting by diff size.

resync Mathlib/Data/Bool/Count
resync Mathlib/Order/Max
resync Mathlib/Algebra/EuclideanDomain/Instances
resync Mathlib/Data/List/Duplicate
resync Mathlib/Data/Multiset/Nodup
resync Mathlib/Data/Set/Pointwise/ListOfFn
resync Mathlib/Dynamics/FixedPoints/Basic
resync Mathlib/Order/OmegaCompletePartialOrder
resync Mathlib/Order/PropInstances
resync Mathlib/Topology/LocallyFinite
resync Mathlib/Data/Bool/Set
resync Mathlib/Data/Fintype/Card
resync Mathlib/Data/Multiset/Bind
resync Mathlib/Data/Rat/Floor
resync Mathlib/Algebra/Order/Floor
resync Mathlib/Data/Int/Basic
resync Mathlib/Data/Int/Dvd/Basic
resync Mathlib/Data/List/Sort
resync Mathlib/Data/Nat/GCD/Basic
resync Mathlib/Data/Set/Enumerate
resync Mathlib/Data/Set/Intervals/OrdConnectedComponent
resync Mathlib/GroupTheory/Subsemigroup/Basic
resync Mathlib/Topology/Connected
resync Mathlib/Topology/NhdsSet
resync Mathlib/Algebra/BigOperators/Multiset/Lemmas
resync Mathlib/Algebra/CharZero/Infinite
resync Mathlib/Data/Multiset/Range
resync Mathlib/Data/Set/Pointwise/Finite

a7eb5ab3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.nhds_set
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
+! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

f7fc89d5

feat: port Topology.NhdsSet (#1875)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

5f8f4e0d

`topology.nhds_set` ⟷ `Mathlib.Topology.NhdsSet`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 7 + 282

topology.nhds_set ⟷ Mathlib.Topology.NhdsSet

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 7 + 282

`topology.nhds_set` ⟷ `Mathlib.Topology.NhdsSet`