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feat(Topology/Algebra/Module/Complement): bundle prodEquivOfIsCompl and quotientEquivOfIsCompl, add ContinuousLinearMap.ofIsTopCompl#39260

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feat(Topology/Algebra/Module/Complement): bundle prodEquivOfIsCompl and quotientEquivOfIsCompl, add ContinuousLinearMap.ofIsTopCompl#39260
sharky564 wants to merge 5 commits into
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This PR completes the three TODO items listed at the top of Mathlib/Topology/Algebra/Module/Complement.lean (introduced in #38547). Submodule.prodEquivOfIsCompl is shown to be a homeomorphism if and only if the two submodules are topological complements. The analogous characterisation for Submodule.quotientEquivOfIsCompl is also provided, and ContinuousLinearMap.ofIsTopCompl is defined as the continuous version of LinearMap.ofIsCompl, taking continuous linear maps from complementary submodules and producing the induced continuous linear map on the whole space.


@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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PR summary 834e51690b

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ IsCompl.isTopCompl_iff_continuous_quotientEquiv
+ IsTopCompl.coe_prodEquiv
+ IsTopCompl.coe_prodEquiv_symm
+ IsTopCompl.coe_quotientEquiv
+ IsTopCompl.coe_quotientEquiv_symm
+ IsTopCompl.prodEquiv
+ IsTopCompl.prodEquiv_apply
+ IsTopCompl.prodEquiv_symm_apply
+ IsTopCompl.quotientEquiv
+ IsTopCompl.quotientEquiv_apply
+ IsTopCompl.quotientEquiv_apply_mk
+ IsTopCompl.quotientEquiv_symm_apply
+ _root_.IsCompl.isTopCompl_iff_continuous_prodEquiv_symm
+ _root_.IsCompl.isTopCompl_iff_isHomeomorph_prodEquiv
+ coe_ofIsTopCompl
+ continuous_prodEquivOfIsCompl
+ ofIsTopCompl
+ ofIsTopCompl_add
+ ofIsTopCompl_apply_left
+ ofIsTopCompl_apply_right
+ ofIsTopCompl_eq
+ ofIsTopCompl_zero
+ range_ofIsTopCompl

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.

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