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Seminorm tvs - #1963

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@mkerjean mkerjean commented May 9, 2026 •

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Motivation for this change

Describing topological vector spaces as vector spaces whose topology is induced by a family of seminorms. Adapting the Hahn-Banach theorem to topological vector spaces. This is necessary to formalise duality theory.

Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers

Reference: How to document

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mkerjean marked this pull request as draft May 9, 2026 11:48
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mkerjean force-pushed the seminorm_tvs branch 2 times, most recently from ebb71fd to b84ab33 Compare June 9, 2026 07:15
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mkerjean force-pushed the seminorm_tvs branch 3 times, most recently from 68ebe3f to 2b89bee Compare July 2, 2026 00:35
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mkerjean marked this pull request as ready for review July 7, 2026 03:09
@affeldt-aist affeldt-aist mentioned this pull request Sep 18, 2026
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mkerjean requested a review from zstone1 September 25, 2026 17:37
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mkerjean force-pushed the seminorm_tvs branch 2 times, most recently from 517c9b8 to 6861d6b Compare October 1, 2026 15:17
@mkerjean

mkerjean commented Oct 1, 2026

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The changelog is broken, i'll fix it asap

Comment thread theories/normedtype_theory/tvs.v Outdated
@affeldt-aist affeldt-aist added this to the 1.20.0 milestone Oct 18, 2026
@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Oct 18, 2026
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(I think that we are almost there but I postpone to the next release that should happen quickly anyway)

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(I think that we are almost there but I postpone to the next release that should happen quickly anyway)

Thank you for your work on this PR. Do tell me how I can help, I can see you did a lot of linting.

Theorem hahn_banach_extension_subctvs (F' : subConvexTvsType F)
(f : {linear F' -> R}) :
(exists2 p : SemiNorm.type V, seminorm_of p & forall z : F', f z <= p (val z)) ->
exists g : {linear_continuous V -> R}, forall x : F', g (val x) = f x.

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@CohenCyril is there a way to not have to write val explicitly?

- adding also initial fam topology, gauge functions, and subbase 0basis
- hahn banach initial_subctvs

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>

Co-authored-by: Cyril Cohen <cyril.cohen@inria.fr>

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