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Linear_continuous structure#1913

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mkerjean wants to merge 12 commits intomath-comp:masterfrom
mkerjean:linear_continuous
Open

Linear_continuous structure#1913
mkerjean wants to merge 12 commits intomath-comp:masterfrom
mkerjean:linear_continuous

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@mkerjean
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@mkerjean mkerjean commented Mar 20, 2026

Motivation for this change

This PR gives the structure of a lmdotype R to:

  • {linear E -> F} when E, F : lmodType R
  • {linear_continuous E -> F} when E F : convextvsType R. It also defined the {linear_continuous _ -> _} structure.

This development is essential to the study of topological duals E' in topological vector spaces, and more generally to the study of closed categories in functional analysis.
Another pull request will enforce the topological structures on {linear_continuous E -> F} ( as a convextvsType, or metric/normed when F is metric or normed).

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

Reference: How to document

Merge policy

As a rule of thumb:

  • PRs with several commits that make sense individually and that
    all compile are preferentially merged into master.
  • PRs with disorganized commits are very likely to be squash-rebased.
Reminder to reviewers

@mkerjean mkerjean closed this Mar 20, 2026
@mkerjean mkerjean reopened this Mar 20, 2026
@mkerjean mkerjean force-pushed the linear_continuous branch 2 times, most recently from 13446e9 to 9c3b607 Compare March 21, 2026 12:56
@mkerjean mkerjean force-pushed the linear_continuous branch from 70ebb90 to 0c4beb3 Compare March 25, 2026 06:49
@mkerjean mkerjean marked this pull request as ready for review March 30, 2026 13:07
@mkerjean mkerjean force-pushed the linear_continuous branch from baafd50 to a319f08 Compare March 31, 2026 11:54
@affeldt-aist
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@CohenCyril could you take a quick look at this PR?
We have been testing it with the Hahn-Banach proof, so it should be mostly ok.

However, we have observed one thing that we would like to address later:
pseudometric_normedZmodType is a morally a topologicalNmodule
but topologicalNmodule is defined later in tvs.v (which imports pseudometric_normed_zmodule.v).
We think that it should be defined at the beginning of pseudometric_normed_zmodule.v and that
pseudometric_normedZmodType should be defined using topologicalNmodule.
We have realized this because of the lemmas such as cvgD/fun_cvgD that we needed to duplicate.
We think that we can make this change and factorize lemmas but we would like to do it in a later PR.
We'll issue about this in the event this PR is merged.

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2 participants