topology.partial | 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

4c19a16e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

34ee86e6

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -90,7 +90,7 @@ theorem pcontinuous_iff' {f : α →. β} :
   have h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x := by
     intro s hs
     have : ptendsto' f (𝓝 x) (𝓝 y) := hf fxy
-    rw [ptendsto'_def] at this 
+    rw [ptendsto'_def] at this
     exact this s hs
   show f.preimage s ∈ 𝓝 x
   apply h'; rw [mem_nhds_iff]; exact ⟨s, Set.Subset.refl _, os, ys⟩

34ee86e6

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2018 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad
 -/
-import Mathbin.Topology.ContinuousOn
-import Mathbin.Order.Filter.Partial
+import Topology.ContinuousOn
+import Order.Filter.Partial
 
 #align_import topology.partial from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"

34ee86e6

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad
-
-! This file was ported from Lean 3 source module topology.partial
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.ContinuousOn
 import Mathbin.Order.Filter.Partial
 
+#align_import topology.partial from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 # Partial functions and topological spaces

34ee86e6

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -68,10 +68,13 @@ def PContinuous (f : α →. β) :=
 #align pcontinuous PContinuous
 -/
 
+#print open_dom_of_pcontinuous /-
 theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.Dom := by
   rw [← PFun.preimage_univ] <;> exact h _ isOpen_univ
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
+-/
 
+#print pcontinuous_iff' /-
 theorem pcontinuous_iff' {f : α →. β} :
     PContinuous f ↔ ∀ {x y} (h : y ∈ f x), PTendsto' f (𝓝 x) (𝓝 y) :=
   by
@@ -95,9 +98,12 @@ theorem pcontinuous_iff' {f : α →. β} :
   show f.preimage s ∈ 𝓝 x
   apply h'; rw [mem_nhds_iff]; exact ⟨s, Set.Subset.refl _, os, ys⟩
 #align pcontinuous_iff' pcontinuous_iff'
+-/
 
+#print continuousWithinAt_iff_ptendsto_res /-
 theorem continuousWithinAt_iff_ptendsto_res (f : α → β) {x : α} {s : Set α} :
     ContinuousWithinAt f s x ↔ PTendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
   tendsto_iff_ptendsto _ _ _ _
 #align continuous_within_at_iff_ptendsto_res continuousWithinAt_iff_ptendsto_res
+-/

34ee86e6

bump to nightly-2023-06-07-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

176da745

Diff

@@ -30,28 +30,28 @@ variable {α β : Type _} [TopologicalSpace α]
 
 #print rtendsto_nhds /-
 theorem rtendsto_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    Rtendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Core s ∈ l :=
+    RTendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Core s ∈ l :=
   all_mem_nhds_filter _ _ (fun s t => id) _
 #align rtendsto_nhds rtendsto_nhds
 -/
 
 #print rtendsto'_nhds /-
 theorem rtendsto'_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    Rtendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Preimage s ∈ l := by rw [rtendsto'_def];
+    RTendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Preimage s ∈ l := by rw [rtendsto'_def];
   apply all_mem_nhds_filter; apply Rel.preimage_mono
 #align rtendsto'_nhds rtendsto'_nhds
 -/
 
 #print ptendsto_nhds /-
 theorem ptendsto_nhds {f : β →. α} {l : Filter β} {a : α} :
-    Ptendsto f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.Core s ∈ l :=
+    PTendsto f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.Core s ∈ l :=
   rtendsto_nhds
 #align ptendsto_nhds ptendsto_nhds
 -/
 
 #print ptendsto'_nhds /-
 theorem ptendsto'_nhds {f : β →. α} {l : Filter β} {a : α} :
-    Ptendsto' f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.Preimage s ∈ l :=
+    PTendsto' f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.Preimage s ∈ l :=
   rtendsto'_nhds
 #align ptendsto'_nhds ptendsto'_nhds
 -/
@@ -73,7 +73,7 @@ theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
 theorem pcontinuous_iff' {f : α →. β} :
-    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) :=
+    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), PTendsto' f (𝓝 x) (𝓝 y) :=
   by
   constructor
   · intro h x y h'
@@ -97,7 +97,7 @@ theorem pcontinuous_iff' {f : α →. β} :
 #align pcontinuous_iff' pcontinuous_iff'
 
 theorem continuousWithinAt_iff_ptendsto_res (f : α → β) {x : α} {s : Set α} :
-    ContinuousWithinAt f s x ↔ Ptendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
+    ContinuousWithinAt f s x ↔ PTendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
   tendsto_iff_ptendsto _ _ _ _
 #align continuous_within_at_iff_ptendsto_res continuousWithinAt_iff_ptendsto_res

34ee86e6

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -90,7 +90,7 @@ theorem pcontinuous_iff' {f : α →. β} :
   have h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x := by
     intro s hs
     have : ptendsto' f (𝓝 x) (𝓝 y) := hf fxy
-    rw [ptendsto'_def] at this
+    rw [ptendsto'_def] at this 
     exact this s hs
   show f.preimage s ∈ 𝓝 x
   apply h'; rw [mem_nhds_iff]; exact ⟨s, Set.Subset.refl _, os, ys⟩

34ee86e6

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -24,7 +24,7 @@ In this file we prove properties of `filter.ptendsto` etc in topological spaces.
 
 open Filter
 
-open Topology
+open scoped Topology
 
 variable {α β : Type _} [TopologicalSpace α]

34ee86e6

bump to nightly-2023-05-28-12

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

7e398081

Diff

@@ -61,19 +61,19 @@ theorem ptendsto'_nhds {f : β →. α} {l : Filter β} {a : α} :
 
 variable [TopologicalSpace β]
 
-#print Pcontinuous /-
+#print PContinuous /-
 /-- Continuity of a partial function -/
-def Pcontinuous (f : α →. β) :=
+def PContinuous (f : α →. β) :=
   ∀ s, IsOpen s → IsOpen (f.Preimage s)
-#align pcontinuous Pcontinuous
+#align pcontinuous PContinuous
 -/
 
-theorem open_dom_of_pcontinuous {f : α →. β} (h : Pcontinuous f) : IsOpen f.Dom := by
+theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.Dom := by
   rw [← PFun.preimage_univ] <;> exact h _ isOpen_univ
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
 theorem pcontinuous_iff' {f : α →. β} :
-    Pcontinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) :=
+    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) :=
   by
   constructor
   · intro h x y h'

34ee86e6

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -68,22 +68,10 @@ def Pcontinuous (f : α →. β) :=
 #align pcontinuous Pcontinuous
 -/
 
-/- warning: open_dom_of_pcontinuous -> open_dom_of_pcontinuous is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {f : PFun.{u1, u2} α β}, (Pcontinuous.{u1, u2} α β _inst_1 _inst_2 f) -> (IsOpen.{u1} α _inst_1 (PFun.Dom.{u1, u2} α β f))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {f : PFun.{u2, u1} α β}, (Pcontinuous.{u2, u1} α β _inst_1 _inst_2 f) -> (IsOpen.{u2} α _inst_1 (PFun.Dom.{u2, u1} α β f))
-Case conversion may be inaccurate. Consider using '#align open_dom_of_pcontinuous open_dom_of_pcontinuousₓ'. -/
 theorem open_dom_of_pcontinuous {f : α →. β} (h : Pcontinuous f) : IsOpen f.Dom := by
   rw [← PFun.preimage_univ] <;> exact h _ isOpen_univ
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
-/- warning: pcontinuous_iff' -> pcontinuous_iff' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {f : PFun.{u1, u2} α β}, Iff (Pcontinuous.{u1, u2} α β _inst_1 _inst_2 f) (forall {x : α} {y : β}, (Membership.Mem.{u2, u2} β (Part.{u2} β) (Part.hasMem.{u2} β) y (f x)) -> (Filter.Ptendsto'.{u1, u2} α β f (nhds.{u1} α _inst_1 x) (nhds.{u2} β _inst_2 y)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {f : PFun.{u2, u1} α β}, Iff (Pcontinuous.{u2, u1} α β _inst_1 _inst_2 f) (forall {x : α} {y : β}, (Membership.mem.{u1, u1} β (Part.{u1} β) (Part.instMembershipPart.{u1} β) y (f x)) -> (Filter.Ptendsto'.{u2, u1} α β f (nhds.{u2} α _inst_1 x) (nhds.{u1} β _inst_2 y)))
-Case conversion may be inaccurate. Consider using '#align pcontinuous_iff' pcontinuous_iff'ₓ'. -/
 theorem pcontinuous_iff' {f : α →. β} :
     Pcontinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) :=
   by
@@ -108,12 +96,6 @@ theorem pcontinuous_iff' {f : α →. β} :
   apply h'; rw [mem_nhds_iff]; exact ⟨s, Set.Subset.refl _, os, ys⟩
 #align pcontinuous_iff' pcontinuous_iff'
 
-/- warning: continuous_within_at_iff_ptendsto_res -> continuousWithinAt_iff_ptendsto_res is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : α -> β) {x : α} {s : Set.{u1} α}, Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_2 f s x) (Filter.Ptendsto.{u1, u2} α β (PFun.res.{u1, u2} α β f s) (nhds.{u1} α _inst_1 x) (nhds.{u2} β _inst_2 (f x)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : α -> β) {x : α} {s : Set.{u2} α}, Iff (ContinuousWithinAt.{u2, u1} α β _inst_1 _inst_2 f s x) (Filter.Ptendsto.{u2, u1} α β (PFun.res.{u2, u1} α β f s) (nhds.{u2} α _inst_1 x) (nhds.{u1} β _inst_2 (f x)))
-Case conversion may be inaccurate. Consider using '#align continuous_within_at_iff_ptendsto_res continuousWithinAt_iff_ptendsto_resₓ'. -/
 theorem continuousWithinAt_iff_ptendsto_res (f : α → β) {x : α} {s : Set α} :
     ContinuousWithinAt f s x ↔ Ptendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
   tendsto_iff_ptendsto _ _ _ _

34ee86e6

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -37,11 +37,8 @@ theorem rtendsto_nhds {r : Rel β α} {l : Filter β} {a : α} :
 
 #print rtendsto'_nhds /-
 theorem rtendsto'_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    Rtendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Preimage s ∈ l :=
-  by
-  rw [rtendsto'_def]
-  apply all_mem_nhds_filter
-  apply Rel.preimage_mono
+    Rtendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.Preimage s ∈ l := by rw [rtendsto'_def];
+  apply all_mem_nhds_filter; apply Rel.preimage_mono
 #align rtendsto'_nhds rtendsto'_nhds
 -/
 
@@ -108,9 +105,7 @@ theorem pcontinuous_iff' {f : α →. β} :
     rw [ptendsto'_def] at this
     exact this s hs
   show f.preimage s ∈ 𝓝 x
-  apply h'
-  rw [mem_nhds_iff]
-  exact ⟨s, Set.Subset.refl _, os, ys⟩
+  apply h'; rw [mem_nhds_iff]; exact ⟨s, Set.Subset.refl _, os, ys⟩
 #align pcontinuous_iff' pcontinuous_iff'
 
 /- warning: continuous_within_at_iff_ptendsto_res -> continuousWithinAt_iff_ptendsto_res is a dubious translation:

34ee86e6

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

4c19a16e

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

@@ -3,8 +3,8 @@ Copyright (c) 2018 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad
 -/
-import Mathlib.Topology.ContinuousOn
 import Mathlib.Order.Filter.Partial
+import Mathlib.Topology.Basic
 
 #align_import topology.partial from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"

4c19a16e

chore(Topology/Partial): rename type variables (#9862)

We use letters X and Y for topological spaces now, not Greek letters.

012256be

Diff

@@ -20,45 +20,45 @@ open Filter
 
 open Topology
 
-variable {α β : Type*} [TopologicalSpace α]
+variable {X Y : Type*} [TopologicalSpace X]
 
-theorem rtendsto_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    RTendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.core s ∈ l :=
+theorem rtendsto_nhds {r : Rel Y X} {l : Filter Y} {x : X} :
+    RTendsto r l (𝓝 x) ↔ ∀ s, IsOpen s → x ∈ s → r.core s ∈ l :=
   all_mem_nhds_filter _ _ (fun _s _t => id) _
 #align rtendsto_nhds rtendsto_nhds
 
-theorem rtendsto'_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    RTendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.preimage s ∈ l := by
+theorem rtendsto'_nhds {r : Rel Y X} {l : Filter Y} {x : X} :
+    RTendsto' r l (𝓝 x) ↔ ∀ s, IsOpen s → x ∈ s → r.preimage s ∈ l := by
   rw [rtendsto'_def]
   apply all_mem_nhds_filter
   apply Rel.preimage_mono
 #align rtendsto'_nhds rtendsto'_nhds
 
-theorem ptendsto_nhds {f : β →. α} {l : Filter β} {a : α} :
-    PTendsto f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.core s ∈ l :=
+theorem ptendsto_nhds {f : Y →. X} {l : Filter Y} {x : X} :
+    PTendsto f l (𝓝 x) ↔ ∀ s, IsOpen s → x ∈ s → f.core s ∈ l :=
   rtendsto_nhds
 #align ptendsto_nhds ptendsto_nhds
 
-theorem ptendsto'_nhds {f : β →. α} {l : Filter β} {a : α} :
-    PTendsto' f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.preimage s ∈ l :=
+theorem ptendsto'_nhds {f : Y →. X} {l : Filter Y} {x : X} :
+    PTendsto' f l (𝓝 x) ↔ ∀ s, IsOpen s → x ∈ s → f.preimage s ∈ l :=
   rtendsto'_nhds
 #align ptendsto'_nhds ptendsto'_nhds
 
 /-! ### Continuity and partial functions -/
 
 
-variable [TopologicalSpace β]
+variable [TopologicalSpace Y]
 
 /-- Continuity of a partial function -/
-def PContinuous (f : α →. β) :=
+def PContinuous (f : X →. Y) :=
   ∀ s, IsOpen s → IsOpen (f.preimage s)
 #align pcontinuous PContinuous
 
-theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.Dom := by
+theorem open_dom_of_pcontinuous {f : X →. Y} (h : PContinuous f) : IsOpen f.Dom := by
   rw [← PFun.preimage_univ]; exact h _ isOpen_univ
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
-theorem pcontinuous_iff' {f : α →. β} :
+theorem pcontinuous_iff' {f : X →. Y} :
     PContinuous f ↔ ∀ {x y} (h : y ∈ f x), PTendsto' f (𝓝 x) (𝓝 y) := by
   constructor
   · intro h x y h'
@@ -83,7 +83,7 @@ theorem pcontinuous_iff' {f : α →. β} :
   exact ⟨s, Set.Subset.refl _, os, ys⟩
 #align pcontinuous_iff' pcontinuous_iff'
 
-theorem continuousWithinAt_iff_ptendsto_res (f : α → β) {x : α} {s : Set α} :
+theorem continuousWithinAt_iff_ptendsto_res (f : X → Y) {x : X} {s : Set X} :
     ContinuousWithinAt f s x ↔ PTendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
   tendsto_iff_ptendsto _ _ _ _
 #align continuous_within_at_iff_ptendsto_res continuousWithinAt_iff_ptendsto_res

4c19a16e

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

@@ -20,7 +20,7 @@ open Filter
 
 open Topology
 
-variable {α β : Type _} [TopologicalSpace α]
+variable {α β : Type*} [TopologicalSpace α]
 
 theorem rtendsto_nhds {r : Rel β α} {l : Filter β} {a : α} :
     RTendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.core s ∈ l :=

4c19a16e

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad
-
-! This file was ported from Lean 3 source module topology.partial
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.ContinuousOn
 import Mathlib.Order.Filter.Partial
 
+#align_import topology.partial from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
 /-!
 # Partial functions and topological spaces

4c19a16e

style: rename Rtendsto and Ptendsto to RTendsto and PTendsto (#4722)

https://github.com/leanprover-community/mathlib4/issues/2203

e0ca1161

Diff

@@ -14,7 +14,7 @@ import Mathlib.Order.Filter.Partial
 /-!
 # Partial functions and topological spaces
 
-In this file we prove properties of `Filter.Ptendsto` etc in topological spaces. We also introduce
+In this file we prove properties of `Filter.PTendsto` etc in topological spaces. We also introduce
 `PContinuous`, a version of `Continuous` for partially defined functions.
 -/
 
@@ -26,24 +26,24 @@ open Topology
 variable {α β : Type _} [TopologicalSpace α]
 
 theorem rtendsto_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    Rtendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.core s ∈ l :=
+    RTendsto r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.core s ∈ l :=
   all_mem_nhds_filter _ _ (fun _s _t => id) _
 #align rtendsto_nhds rtendsto_nhds
 
 theorem rtendsto'_nhds {r : Rel β α} {l : Filter β} {a : α} :
-    Rtendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.preimage s ∈ l := by
+    RTendsto' r l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → r.preimage s ∈ l := by
   rw [rtendsto'_def]
   apply all_mem_nhds_filter
   apply Rel.preimage_mono
 #align rtendsto'_nhds rtendsto'_nhds
 
 theorem ptendsto_nhds {f : β →. α} {l : Filter β} {a : α} :
-    Ptendsto f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.core s ∈ l :=
+    PTendsto f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.core s ∈ l :=
   rtendsto_nhds
 #align ptendsto_nhds ptendsto_nhds
 
 theorem ptendsto'_nhds {f : β →. α} {l : Filter β} {a : α} :
-    Ptendsto' f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.preimage s ∈ l :=
+    PTendsto' f l (𝓝 a) ↔ ∀ s, IsOpen s → a ∈ s → f.preimage s ∈ l :=
   rtendsto'_nhds
 #align ptendsto'_nhds ptendsto'_nhds
 
@@ -62,7 +62,7 @@ theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
 theorem pcontinuous_iff' {f : α →. β} :
-    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) := by
+    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), PTendsto' f (𝓝 x) (𝓝 y) := by
   constructor
   · intro h x y h'
     simp only [ptendsto'_def, mem_nhds_iff]
@@ -77,7 +77,7 @@ theorem pcontinuous_iff' {f : α →. β} :
   apply mem_of_superset _ h
   have h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x := by
     intro s hs
-    have : Ptendsto' f (𝓝 x) (𝓝 y) := hf fxy
+    have : PTendsto' f (𝓝 x) (𝓝 y) := hf fxy
     rw [ptendsto'_def] at this
     exact this s hs
   show f.preimage s ∈ 𝓝 x
@@ -87,6 +87,6 @@ theorem pcontinuous_iff' {f : α →. β} :
 #align pcontinuous_iff' pcontinuous_iff'
 
 theorem continuousWithinAt_iff_ptendsto_res (f : α → β) {x : α} {s : Set α} :
-    ContinuousWithinAt f s x ↔ Ptendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
+    ContinuousWithinAt f s x ↔ PTendsto (PFun.res f s) (𝓝 x) (𝓝 (f x)) :=
   tendsto_iff_ptendsto _ _ _ _
 #align continuous_within_at_iff_ptendsto_res continuousWithinAt_iff_ptendsto_res

4c19a16e

chore: rename Pcontinuous to PContinuous (#4428)

ref #4354

3ff6ded9

Diff

@@ -15,7 +15,7 @@ import Mathlib.Order.Filter.Partial
 # Partial functions and topological spaces
 
 In this file we prove properties of `Filter.Ptendsto` etc in topological spaces. We also introduce
-`Pcontinuous`, a version of `Continuous` for partially defined functions.
+`PContinuous`, a version of `Continuous` for partially defined functions.
 -/
 
 
@@ -53,16 +53,16 @@ theorem ptendsto'_nhds {f : β →. α} {l : Filter β} {a : α} :
 variable [TopologicalSpace β]
 
 /-- Continuity of a partial function -/
-def Pcontinuous (f : α →. β) :=
+def PContinuous (f : α →. β) :=
   ∀ s, IsOpen s → IsOpen (f.preimage s)
-#align pcontinuous Pcontinuous
+#align pcontinuous PContinuous
 
-theorem open_dom_of_pcontinuous {f : α →. β} (h : Pcontinuous f) : IsOpen f.Dom := by
+theorem open_dom_of_pcontinuous {f : α →. β} (h : PContinuous f) : IsOpen f.Dom := by
   rw [← PFun.preimage_univ]; exact h _ isOpen_univ
 #align open_dom_of_pcontinuous open_dom_of_pcontinuous
 
 theorem pcontinuous_iff' {f : α →. β} :
-    Pcontinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) := by
+    PContinuous f ↔ ∀ {x y} (h : y ∈ f x), Ptendsto' f (𝓝 x) (𝓝 y) := by
   constructor
   · intro h x y h'
     simp only [ptendsto'_def, mem_nhds_iff]

4c19a16e

feat: Port/Topology.Partial (#2081)

port of topology.partial

only basic naming fixes

24c3d9ba

`topology.partial` ⟷ `Mathlib.Topology.Partial`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7 + 292

topology.partial ⟷ Mathlib.Topology.Partial

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7 + 292

`topology.partial` ⟷ `Mathlib.Topology.Partial`