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[Merged by Bors] - feat: the left uniformity in a group#35252

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[Merged by Bors] - feat: the left uniformity in a group#35252
sgouezel wants to merge 8 commits intoleanprover-community:masterfrom
sgouezel:SG_leftUniform

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@sgouezel sgouezel commented Feb 13, 2026 •
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We have currently a specific definition of the right uniformity of a topological group, but not of the left uniformity. We introduce it in the current PR, for two reasons. First, there is no reason to favor one over the other. Second, it is needed in #35037, which changes the formula for the distance in a normed group to make it left-invariant following standard conventions.

We also prove that a group is complete for its left-uniformity iff it is complete for its right-uniformity, by showing that inversion is a uniform equivalence between the two uniformities.

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github-actions bot commented Feb 13, 2026 •
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PR summary 43d5379b32

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ Homeomorph.symm_inv
+ IsTopologicalGroup.completeSpace_rightUniformSpace_iff_leftUniformSpace
+ IsTopologicalGroup.leftUniformSpace
+ QuotientGroup.completeSpace_left
+ QuotientGroup.completeSpace_left'
+ QuotientGroup.completeSpace_right
+ QuotientGroup.completeSpace_right'
+ UniformEquiv.inv
+ comap_inv_leftUniformSpace
+ comap_op_leftUniformSpace
+ comap_op_rightUniformSpace
+ mul_inv_mul_mul_cancel
+ mul_mul_inv_mul_cancel
+ nhds_translation_inv_mul
+ opUniformEquivLeft
+ opUniformEquivRight
+ uniformity_eq_comap_nhds_one_left
- QuotientGroup.completeSpace
- QuotientGroup.completeSpace'

You can run this locally as follows 
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-topology Topological spaces, uniform spaces, metric spaces, filters label Feb 13, 2026
urkud
urkud reviewed Feb 15, 2026
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Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean Outdated
variable {ι : Type*} {l : Filter ι} {l' : Filter β} {f f' : ι → β → α} {g g' : β → α} {s : Set β}

@[to_additive]
@[to_additive (attr := to_fun)]
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Are these changes related to (needed for) the main topic of this PR?

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@sgouezel sgouezel Feb 15, 2026

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No. Let me move them to another PR.

@sgouezel sgouezel mentioned this pull request Feb 15, 2026
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urkud commented Feb 16, 2026

Could you please fix CI, then bench it? Otherwise LGTM. Thanks!

@mathlib-dependent-issues mathlib-dependent-issues bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Feb 16, 2026
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sgouezel commented Feb 16, 2026

!bench

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leanprover-radar commented Feb 16, 2026 •
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Benchmark results for 31a5330 against 43d5379 are in! @sgouezel

  • 🟥 build//instructions: +16.3G (+0.01%)

Small changes (3🟥)

  • 🟥 build/module/Mathlib.Tactic.FailIfNoProgress//instructions: +296.3M (+5.33%)
  • 🟥 build/module/Mathlib.Topology.Algebra.IsUniformGroup.Basic//instructions: +5.0G (+12.01%) (reduced significance based on *//lines)
  • 🟥 build/module/Mathlib.Topology.Algebra.IsUniformGroup.Defs//instructions: +1.2G (+2.84%)

@mathlib-dependent-issues mathlib-dependent-issues bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Feb 16, 2026
j-loreaux
j-loreaux reviewed Feb 16, 2026
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Thanks!

bors d+

Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean Outdated
Comment on lines 756 to 758
In the most common use case ─ quotients of normed additive commutative groups by subgroups ─
significant care was taken so that the uniform structure inherent in that setting coincides
(definitionally) with the uniform structure provided here. -/]
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Isn't this not (yet) true because the quotient is equipped with the right uniformity (for now)?

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Yes, this is premature. Removed. thanks!

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mathlib-bors bot commented Feb 16, 2026

✌️ sgouezel can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@mathlib-triage mathlib-triage bot added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Feb 16, 2026
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sgouezel commented Feb 16, 2026

bors r+

@mathlib-triage mathlib-triage bot added the ready-to-merge This PR has been sent to bors. label Feb 16, 2026
mathlib-bors bot pushed a commit that referenced this pull request Feb 16, 2026
@sgouezel
feat: the left uniformity in a group (#35252)
32fe3f9 
We have currently a specific definition of the right uniformity of a topological group, but not of the left uniformity. We introduce it in the current PR, for two reasons. First, there is no reason to favor one over the other. Second, it is needed in #35037, which changes the formula for the distance in a normed group to make it left-invariant following standard conventions.

We also prove that a group is complete for its left-uniformity iff it is complete for its right-uniformity, by showing that inversion is a uniform equivalence between the two uniformities.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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mathlib-bors bot commented Feb 16, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: the left uniformity in a group [Merged by Bors] - feat: the left uniformity in a group Feb 16, 2026
@mathlib-bors mathlib-bors bot closed this Feb 16, 2026
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