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[Merged by Bors] - feat: equivalent characterisation of split continuous linear maps#35057

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grunweg:splits-equivalent
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[Merged by Bors] - feat: equivalent characterisation of split continuous linear maps#35057
grunweg wants to merge 28 commits intoleanprover-community:masterfrom
grunweg:splits-equivalent

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@grunweg grunweg commented Feb 9, 2026

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
f admits a continuous left inverse iff it is injective, has closed range and range f has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.


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github-actions bot commented Feb 9, 2026

PR summary 91fb523cd9

Import changes exceeding 2%

% File
+3.61% Mathlib.Analysis.Normed.Module.ContinuousInverse

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Analysis.Normed.Module.ContinuousInverse 1910 1979 +69 (+3.61%)
Import changes for all files
Files Import difference
Mathlib.Analysis.Normed.Module.ContinuousInverse 69

Declarations diff

+ antilipschitzConstant_of_injective_of_isClosed_range
+ antilipschitz_antiLipschitzConstant_of_injective_of_isClosed_range
+ closedComplemented_range
+ exists_isClosed_isCompl
+ isClosed
+ isClosed_range
+ leftInverse_of_injective_of_isClosed_range
+ of_injective_of_isClosed_range_of_closedComplement_range
+ range_eq_ker_of_leftInverse
+ range_toLinearMap
++ complement
++ isClosed_complement
++ isCompl_complement
- ClosedComplemented.exists_isClosed_isCompl
- ClosedComplemented.isClosed

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).

@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 9, 2026
@grunweg grunweg added the t-analysis Analysis (normed *, calculus) label Feb 9, 2026
@grunweg grunweg mentioned this pull request Feb 10, 2026
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@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 11, 2026
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@chrisflav chrisflav added the awaiting-author A reviewer has asked the author a question or requested changes. label Feb 15, 2026
@grunweg grunweg removed the awaiting-author A reviewer has asked the author a question or requested changes. label Feb 18, 2026
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grunweg commented Feb 20, 2026

This PR is ready for review again.

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This is nice, thanks!

bors merge

mathlib-bors bot pushed a commit that referenced this pull request Feb 24, 2026
…5057)

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
f admits a continuous left inverse iff it splits, i.e. is injective, has closed range and range f has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.
@mathlib-triage mathlib-triage bot added the ready-to-merge This PR has been sent to bors. label Feb 24, 2026
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mathlib-bors bot commented Feb 24, 2026

Build failed:

@grunweg grunweg added the auto-merge-after-CI Please do not add manually. Requests for a bot to merge automatically once CI is done. label Feb 25, 2026
@github-actions github-actions bot added the large-import Automatically added label for PRs with a significant increase in transitive imports label Feb 27, 2026
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As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

mathlib-bors bot pushed a commit that referenced this pull request Feb 27, 2026
…5057)

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
`f` admits a continuous left inverse iff it is injective, has closed range and `range f` has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.
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mathlib-bors bot commented Feb 27, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: equivalent characterisation of split continuous linear maps [Merged by Bors] - feat: equivalent characterisation of split continuous linear maps Feb 27, 2026
@mathlib-bors mathlib-bors bot closed this Feb 27, 2026
@grunweg grunweg deleted the splits-equivalent branch February 28, 2026 15:52
pfaffelh pushed a commit to pfaffelh/mathlib4 that referenced this pull request Mar 2, 2026
…anprover-community#35057)

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
`f` admits a continuous left inverse iff it is injective, has closed range and `range f` has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.
xroblot pushed a commit to xroblot/mathlib4 that referenced this pull request Mar 10, 2026
…anprover-community#35057)

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
`f` admits a continuous left inverse iff it is injective, has closed range and `range f` has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.
pevogam pushed a commit to pevogam/mathlib4 that referenced this pull request Mar 19, 2026
…anprover-community#35057)

We add an equivalent characterisation of continuous linear maps with a continuous left inverse:
`f` admits a continuous left inverse iff it is injective, has closed range and `range f` has a closed complement.

This equivalence is used for extracting an explicit complement for immersions, hence transitively for proving that immersions are closed under composition.

From the path towards immersions, submersions and embedded submanifolds.
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