[Merged by Bors] - feat(Analysis/LocallyConvex/Polar): Calculate the polar of a set closed under scalar multiplication#14458
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[Merged by Bors] - feat(Analysis/LocallyConvex/Polar): Calculate the polar of a set closed under scalar multiplication#14458
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PR summary 98c18162a1Import changes for modified filesNo significant changes to the import graph Import changes for all files
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urkud
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Jul 13, 2024
urkud
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Jul 13, 2024
| exact zero_le_one | ||
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| /-- The polar of a set closed under scalar multiplication as a submodule -/ | ||
| def polarSubmodule (m : SubMulAction 𝕜 E) : Submodule 𝕜 F := |
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Do we have {y | ∀ x ∈ m, B x y = 0} (a.k.a. the intersection of all (B x).ker) as a submodule for any set (can't find it)? If yes, then we should have a lemma saying that polar is equal to this set instead of adding a new definition. If no, then please ask on Zulip if we should add it or go ahead with polarSubmodule.
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urkud
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Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
urkud
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urkud
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Jul 15, 2024
urkud
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Jul 15, 2024
Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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Thanks! 🎉 |
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Build failed (retrying...): |
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Pull request successfully merged into master. Build succeeded: |
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The polar of a set closed under scalar multiplication the set of functionals vanishing on the set.
In particular this applies to submodules.
Example application: #14369