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feat: prove strict group homs are stable under Prod.map#39270

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feat: prove strict group homs are stable under Prod.map#39270
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This PR proves that strict group homomorphisms are stable under product maps.

It adds an auxiliary lemma showing that the range restriction of a strict group homomorphism is an open quotient map, and uses it to prove that MonoidHom.prodMap preserves Topology.IsStrictMap.

Towards #38421.

Add section for properties of strict maps between topological groups and related theorems.
@github-actions github-actions Bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label May 12, 2026
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Welcome new contributor!

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@github-actions github-actions Bot added the t-topology Topological spaces, uniform spaces, metric spaces, filters label May 12, 2026
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PR summary 13338c3c40

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Topology.Algebra.Group.Basic 1064 1065 +1 (+0.09%)
Import changes for all files
Files Import difference
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1

Declarations diff

+ MonoidHom.isOpenQuotientMap_of_strictMap
+ prodMap

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.


No changes to strong technical debt.
No changes to weak technical debt.

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new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! t-topology Topological spaces, uniform spaces, metric spaces, filters

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