topology.algebra.group.compact | 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)

Changes in mathlib3port

mathlib3

mathlib3port

23aa88e3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
 -/
-import Mathbin.Topology.Algebra.Group.Basic
-import Mathbin.Topology.CompactOpen
-import Mathbin.Topology.Sets.Compacts
+import Topology.Algebra.Group.Basic
+import Topology.CompactOpen
+import Topology.Sets.Compacts
 
 #align_import topology.algebra.group.compact from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"

23aa88e3

bump to nightly-2023-09-05-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

c99d0889

Diff

@@ -44,7 +44,7 @@ is locally compact. -/
 theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
     (K : PositiveCompacts G) : LocallyCompactSpace G :=
   by
-  refine' locally_compact_of_compact_nhds fun x => _
+  refine' WeaklyLocallyCompactSpace.locallyCompactSpace fun x => _
   obtain ⟨y, hy⟩ := K.interior_nonempty
   let F := Homeomorph.mulLeft (x * y⁻¹)
   refine' ⟨F '' K, _, K.is_compact.image F.continuous⟩

23aa88e3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.group.compact
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Group.Basic
 import Mathbin.Topology.CompactOpen
 import Mathbin.Topology.Sets.Compacts
 
+#align_import topology.algebra.group.compact from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
+
 /-!
 # Additional results on topological groups

23aa88e3

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -39,12 +39,12 @@ section
 
 variable [TopologicalSpace G] [Group G] [TopologicalGroup G]
 
-#print TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group /-
+#print TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group /-
 /-- Every separated topological group in which there exists a compact set with nonempty interior
 is locally compact. -/
 @[to_additive
       "Every separated topological group in which there exists a compact set with nonempty\ninterior is locally compact."]
-theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space G]
+theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
     (K : PositiveCompacts G) : LocallyCompactSpace G :=
   by
   refine' locally_compact_of_compact_nhds fun x => _
@@ -56,8 +56,8 @@ theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space
   have : F.symm x = y := by simp [F, Homeomorph.mulLeft_symm]
   rw [this]
   exact mem_interior_iff_mem_nhds.1 hy
-#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group
-#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_AddGroup
+#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
+#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup
 -/
 
 end

23aa88e3

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ imports developing either positive compacts or the compact open topology.
 
 open Classical Set Filter TopologicalSpace Function
 
-open Classical Topology Filter Pointwise
+open scoped Classical Topology Filter Pointwise
 
 universe u v w x

23aa88e3

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -51,9 +51,7 @@ theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space
   obtain ⟨y, hy⟩ := K.interior_nonempty
   let F := Homeomorph.mulLeft (x * y⁻¹)
   refine' ⟨F '' K, _, K.is_compact.image F.continuous⟩
-  suffices F.symm ⁻¹' K ∈ 𝓝 x by
-    convert this
-    apply Equiv.image_eq_preimage
+  suffices F.symm ⁻¹' K ∈ 𝓝 x by convert this; apply Equiv.image_eq_preimage
   apply ContinuousAt.preimage_mem_nhds F.symm.continuous.continuous_at
   have : F.symm x = y := by simp [F, Homeomorph.mulLeft_symm]
   rw [this]

23aa88e3

bump to nightly-2023-02-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

5c91f1b0

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.algebra.group.compact
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Sets.Compacts
 /-!
 # Additional results on topological groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Two results on topological groups that have been separated out as they require more substantial
 imports developing either positive compacts or the compact open topology.

f2ce6086

bump to nightly-2023-02-22-00

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

7c6a5463

Diff

@@ -36,11 +36,12 @@ section
 
 variable [TopologicalSpace G] [Group G] [TopologicalGroup G]
 
+#print TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group /-
 /-- Every separated topological group in which there exists a compact set with nonempty interior
 is locally compact. -/
 @[to_additive
       "Every separated topological group in which there exists a compact set with nonempty\ninterior is locally compact."]
-theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
+theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space G]
     (K : PositiveCompacts G) : LocallyCompactSpace G :=
   by
   refine' locally_compact_of_compact_nhds fun x => _
@@ -54,8 +55,9 @@ theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space
   have : F.symm x = y := by simp [F, Homeomorph.mulLeft_symm]
   rw [this]
   exact mem_interior_iff_mem_nhds.1 hy
-#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
-#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_add_group
+#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group
+#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_AddGroup
+-/
 
 end
 
@@ -63,6 +65,7 @@ section Quotient
 
 variable [Group G] [TopologicalSpace G] [TopologicalGroup G] {Γ : Subgroup G}
 
+#print QuotientGroup.continuousSMul /-
 @[to_additive]
 instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G (G ⧸ Γ)
     where continuous_smul :=
@@ -75,7 +78,8 @@ instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G
       refine' continuous_coinduced_rng.comp continuous_mul
     exact QuotientMap.continuous_lift_prod_right quotientMap_quotient_mk' H
 #align quotient_group.has_continuous_smul QuotientGroup.continuousSMul
-#align quotient_add_group.has_continuous_vadd quotientAddGroup.has_continuous_vadd
+#align quotient_add_group.has_continuous_vadd QuotientAddGroup.continuousVAdd
+-/
 
 end Quotient

f2ce6086

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: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -18,9 +18,11 @@ imports developing either positive compacts or the compact open topology.
 -/
 
 
-open Classical Set Filter TopologicalSpace Function
+open scoped Classical
+open Set Filter TopologicalSpace Function
 
-open Classical Topology Filter Pointwise
+open scoped Classical
+open Topology Filter Pointwise
 
 universe u v w x

f2ce6086

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -55,7 +55,7 @@ instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G
     change Continuous F
     have H : Continuous (F ∘ fun p : G × G => (p.1, QuotientGroup.mk p.2)) := by
       change Continuous fun p : G × G => QuotientGroup.mk (p.1 * p.2)
-      refine' continuous_coinduced_rng.comp continuous_mul
+      exact continuous_coinduced_rng.comp continuous_mul
     exact QuotientMap.continuous_lift_prod_right quotientMap_quotient_mk' H
 #align quotient_group.has_continuous_smul QuotientGroup.continuousSMul
 #align quotient_add_group.has_continuous_vadd QuotientAddGroup.continuousVAdd

f2ce6086

feat(Topology/Separation): define R₁ spaces, review API (#10085)

Main API changes

Define R1Space, a.k.a. preregular space.
Drop T2OrLocallyCompactRegularSpace.
Generalize all existing theorems about T2OrLocallyCompactRegularSpace to R1Space.
Drop the [T2OrLocallyCompactRegularSpace _] assumption if the space is known to be regular for other reason (e.g., because it's a topological group).

New theorems

Specializes.not_disjoint: if x ⤳ y, then 𝓝 x and 𝓝 y aren't disjoint;
specializes_iff_not_disjoint, Specializes.inseparable, disjoint_nhds_nhds_iff_not_inseparable, r1Space_iff_inseparable_or_disjoint_nhds: basic API about R1Spaces;
Inducing.r1Space, R1Space.induced, R1Space.sInf, R1Space.iInf, R1Space.inf, instances for Subtype _, X × Y, and ∀ i, X i: basic instances for R1Space;
IsCompact.mem_closure_iff_exists_inseparable, IsCompact.closure_eq_biUnion_inseparable: characterizations of the closure of a compact set in a preregular space;
Inseparable.mem_measurableSet_iff: topologically inseparable points can't be separated by a Borel measurable set;
IsCompact.closure_subset_measurableSet, IsCompact.measure_closure: in a preregular space, a measurable superset of a compact set includes its closure as well; as a corollary, closure K has the same measure as K.
exists_mem_nhds_isCompact_mapsTo_of_isCompact_mem_nhds: an auxiliary lemma extracted from a LocallyCompactPair instance;
IsCompact.isCompact_isClosed_basis_nhds: if x admits a compact neighborhood, then it admits a basis of compact closed neighborhoods; in particular, a weakly locally compact preregular space is a locally compact regular space;
isCompact_isClosed_basis_nhds: a version of the previous theorem for weakly locally compact spaces;
exists_mem_nhds_isCompact_isClosed: in a locally compact regular space, each point admits a compact closed neighborhood.

Deprecated theorems

Some theorems about topological groups are true for any (pre)regular space, so we deprecate the special cases.

exists_isCompact_isClosed_subset_isCompact_nhds_one: use new IsCompact.isCompact_isClosed_basis_nhds instead;
instLocallyCompactSpaceOfWeaklyOfGroup, instLocallyCompactSpaceOfWeaklyOfAddGroup: are now implied by WeaklyLocallyCompactSpace.locallyCompactSpace;
local_isCompact_isClosed_nhds_of_group, local_isCompact_isClosed_nhds_of_addGroup: use isCompact_isClosed_basis_nhds instead;
exists_isCompact_isClosed_nhds_one, exists_isCompact_isClosed_nhds_zero: use exists_mem_nhds_isCompact_isClosed instead.

Renamed/moved theorems

For each renamed theorem, the old theorem is redefined as a deprecated alias.

isOpen_setOf_disjoint_nhds_nhds: moved to Constructions;
isCompact_closure_of_subset_compact -> IsCompact.closure_of_subset;
IsCompact.measure_eq_infi_isOpen -> IsCompact.measure_eq_iInf_isOpen;
exists_compact_superset_iff -> exists_isCompact_superset_iff;
separatedNhds_of_isCompact_isCompact_isClosed -> SeparatedNhds.of_isCompact_isCompact_isClosed;
separatedNhds_of_isCompact_isCompact -> SeparatedNhds.of_isCompact_isCompact;
separatedNhds_of_finset_finset -> SeparatedNhds.of_finset_finset;
point_disjoint_finset_opens_of_t2 -> SeparatedNhds.of_singleton_finset;
separatedNhds_of_isCompact_isClosed -> SeparatedNhds.of_isCompact_isClosed;
exists_open_superset_and_isCompact_closure -> exists_isOpen_superset_and_isCompact_closure;
exists_open_with_compact_closure -> exists_isOpen_mem_isCompact_closure;

7458f0e7

Diff

@@ -36,15 +36,9 @@ is locally compact. -/
   "Every topological additive group
   in which there exists a compact set with nonempty interior is locally compact."]
 theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
-    (K : PositiveCompacts G) : LocallyCompactSpace G := by
-  have A : WeaklyLocallyCompactSpace G :=
-    { exists_compact_mem_nhds := by
-        intro x
-        obtain ⟨y, hy⟩ := K.interior_nonempty
-        refine ⟨(x * y⁻¹) • (K : Set G), K.isCompact.smul _, ?_⟩
-        rw [mem_interior_iff_mem_nhds] at hy
-        simpa using smul_mem_nhds (x * y⁻¹) hy }
-  infer_instance
+    (K : PositiveCompacts G) : LocallyCompactSpace G :=
+  let ⟨_x, hx⟩ := K.interior_nonempty
+  K.isCompact.locallyCompactSpace_of_mem_nhds_of_group (mem_interior_iff_mem_nhds.1 hx)
 #align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
 #align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup

f2ce6086

feat: construct Haar measure in locally compact non-Hausdorff groups (#9746)

The construction we have is given in T2 spaces, but it works in non-Hausdorff spaces modulo a few modifications.

For this, we introduce an ad hoc class T2OrLocallyCompactRegularSpace, which is just enough to unify the arguments, as a replacement for the class ClosableCompactSubsetOpenSpace (which is not strong enough). In the file Separation.lean, we move some material that was only available on T2 spaces to this new class.

The construction is needed for a forthcoming improvement of uniqueness results for Haar measures, based on https://mathoverflow.net/questions/456670/uniqueness-of-left-invariant-borel-probability-measure-on-compact-groups.

158d8524

Diff

@@ -31,26 +31,20 @@ section
 variable [TopologicalSpace G] [Group G] [TopologicalGroup G]
 
 /-- Every topological group in which there exists a compact set with nonempty interior
-is weakly locally compact. -/
-@[to_additive
-  "Every separated topological additive group
-  in which there exists a compact set with nonempty interior is weakly locally compact."]
-theorem TopologicalSpace.PositiveCompacts.weaklyLocallyCompactSpace_of_group
-    (K : PositiveCompacts G) : WeaklyLocallyCompactSpace G where
-  exists_compact_mem_nhds x := by
-    obtain ⟨y, hy⟩ := K.interior_nonempty
-    refine ⟨(x * y⁻¹) • (K : Set G), K.isCompact.smul _, ?_⟩
-    rw [mem_interior_iff_mem_nhds] at hy
-    simpa using smul_mem_nhds (x * y⁻¹) hy
-
-/-- Every separated topological group in which there exists a compact set with nonempty interior
 is locally compact. -/
 @[to_additive
-  "Every separated topological additive group
+  "Every topological additive group
   in which there exists a compact set with nonempty interior is locally compact."]
-theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
-    (K : PositiveCompacts G) : LocallyCompactSpace G :=
-  have := K.weaklyLocallyCompactSpace_of_group; inferInstance
+theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
+    (K : PositiveCompacts G) : LocallyCompactSpace G := by
+  have A : WeaklyLocallyCompactSpace G :=
+    { exists_compact_mem_nhds := by
+        intro x
+        obtain ⟨y, hy⟩ := K.interior_nonempty
+        refine ⟨(x * y⁻¹) • (K : Set G), K.isCompact.smul _, ?_⟩
+        rw [mem_interior_iff_mem_nhds] at hy
+        simpa using smul_mem_nhds (x * y⁻¹) hy }
+  infer_instance
 #align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
 #align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup

f2ce6086

feat: define weakly locally compact spaces (#6770)

8c47c403

Diff

@@ -30,25 +30,27 @@ section
 
 variable [TopologicalSpace G] [Group G] [TopologicalGroup G]
 
+/-- Every topological group in which there exists a compact set with nonempty interior
+is weakly locally compact. -/
+@[to_additive
+  "Every separated topological additive group
+  in which there exists a compact set with nonempty interior is weakly locally compact."]
+theorem TopologicalSpace.PositiveCompacts.weaklyLocallyCompactSpace_of_group
+    (K : PositiveCompacts G) : WeaklyLocallyCompactSpace G where
+  exists_compact_mem_nhds x := by
+    obtain ⟨y, hy⟩ := K.interior_nonempty
+    refine ⟨(x * y⁻¹) • (K : Set G), K.isCompact.smul _, ?_⟩
+    rw [mem_interior_iff_mem_nhds] at hy
+    simpa using smul_mem_nhds (x * y⁻¹) hy
+
 /-- Every separated topological group in which there exists a compact set with nonempty interior
 is locally compact. -/
 @[to_additive
-      "Every separated topological group in which there exists a compact set with nonempty
-      interior is locally compact."]
+  "Every separated topological additive group
+  in which there exists a compact set with nonempty interior is locally compact."]
 theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
-    (K : PositiveCompacts G) : LocallyCompactSpace G := by
-  refine' locally_compact_of_compact_nhds fun x => _
-  obtain ⟨y, hy⟩ := K.interior_nonempty
-  let F := Homeomorph.mulLeft (x * y⁻¹)
-  refine' ⟨F '' K, _, K.isCompact.image F.continuous⟩
-  suffices F.symm ⁻¹' K ∈ 𝓝 x by
-    convert this using 1
-    apply Equiv.image_eq_preimage
-  apply ContinuousAt.preimage_mem_nhds F.symm.continuous.continuousAt
-  have : F.symm x = y := by simp only [Homeomorph.mulLeft_symm, mul_inv_rev,
-      inv_inv, Homeomorph.coe_mulLeft, inv_mul_cancel_right]
-  rw [this]
-  exact mem_interior_iff_mem_nhds.1 hy
+    (K : PositiveCompacts G) : LocallyCompactSpace G :=
+  have := K.weaklyLocallyCompactSpace_of_group; inferInstance
 #align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
 #align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup
 
@@ -59,8 +61,7 @@ section Quotient
 variable [Group G] [TopologicalSpace G] [TopologicalGroup G] {Γ : Subgroup G}
 
 @[to_additive]
-instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G (G ⧸ Γ)
-    where
+instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G (G ⧸ Γ) where
   continuous_smul := by
     let F : G × G ⧸ Γ → G ⧸ Γ := fun p => p.1 • p.2
     change 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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.group.compact
-! 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.Algebra.Group.Basic
 import Mathlib.Topology.CompactOpen
 import Mathlib.Topology.Sets.Compacts
 
+#align_import topology.algebra.group.compact from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Additional results on topological groups

f2ce6086

feat(Topology/Algebra/Group/Basic): product of compact set and closed set is closed (#5471)

Also adds the version for group actions, and the consequence that if we quotient by a compact subgroup then the quotient map is closed.

I also made some syntax tweaks in some places, mainly making use of our great new implicit functions.

52336fd7

Diff

@@ -31,9 +31,6 @@ variable {α : Type u} {β : Type v} {G : Type w} {H : Type x}
 
 section
 
-/-! Some results about an open set containing the product of two sets in a topological group. -/
-
-
 variable [TopologicalSpace G] [Group G] [TopologicalGroup G]
 
 /-- Every separated topological group in which there exists a compact set with nonempty interior

f2ce6086

feat: port MeasureTheory.Measure.Haar.Basic (#4517)

This PR also rename locallyCompactSpace_of_Group to locallyCompactSpace_of_group, and add a reference to the issue in MeasureTheory.Group.Measure.

422af61d

Diff

@@ -41,7 +41,7 @@ is locally compact. -/
 @[to_additive
       "Every separated topological group in which there exists a compact set with nonempty
       interior is locally compact."]
-theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space G]
+theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group [T2Space G]
     (K : PositiveCompacts G) : LocallyCompactSpace G := by
   refine' locally_compact_of_compact_nhds fun x => _
   obtain ⟨y, hy⟩ := K.interior_nonempty
@@ -55,8 +55,8 @@ theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space
       inv_inv, Homeomorph.coe_mulLeft, inv_mul_cancel_right]
   rw [this]
   exact mem_interior_iff_mem_nhds.1 hy
-#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group
-#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_AddGroup
+#align topological_space.positive_compacts.locally_compact_space_of_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_group
+#align topological_space.positive_compacts.locally_compact_space_of_add_group TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup
 
 end

f2ce6086

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -70,8 +70,7 @@ instance QuotientGroup.continuousSMul [LocallyCompactSpace G] : ContinuousSMul G
   continuous_smul := by
     let F : G × G ⧸ Γ → G ⧸ Γ := fun p => p.1 • p.2
     change Continuous F
-    have H : Continuous (F ∘ fun p : G × G => (p.1, QuotientGroup.mk p.2)) :=
-      by
+    have H : Continuous (F ∘ fun p : G × G => (p.1, QuotientGroup.mk p.2)) := by
       change Continuous fun p : G × G => QuotientGroup.mk (p.1 * p.2)
       refine' continuous_coinduced_rng.comp continuous_mul
     exact QuotientMap.continuous_lift_prod_right quotientMap_quotient_mk' H

f2ce6086

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -48,7 +48,7 @@ theorem TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_Group [T2Space
   let F := Homeomorph.mulLeft (x * y⁻¹)
   refine' ⟨F '' K, _, K.isCompact.image F.continuous⟩
   suffices F.symm ⁻¹' K ∈ 𝓝 x by
-    convert this
+    convert this using 1
     apply Equiv.image_eq_preimage
   apply ContinuousAt.preimage_mem_nhds F.symm.continuous.continuousAt
   have : F.symm x = y := by simp only [Homeomorph.mulLeft_symm, mul_inv_rev,

f2ce6086

feat: Port/Topology.Algebra.Group.Compact (#2420)

e94a78db

`topology.algebra.group.compact` ⟷ `Mathlib.Topology.Algebra.Group.Compact`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Main API changes

New theorems

Deprecated theorems

Renamed/moved theorems

Dependencies 9 + 399

topology.algebra.group.compact ⟷ Mathlib.Topology.Algebra.Group.Compact

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Main API changes

New theorems

Deprecated theorems

Renamed/moved theorems

Dependencies 9 + 399

`topology.algebra.group.compact` ⟷ `Mathlib.Topology.Algebra.Group.Compact`