[Merged by Bors] - feat: Mapping extreme points under continuous maps #8574
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Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit.
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Mathlib/Analysis/Convex/Extreme.lean
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| section OrderedRing | ||
| variable [OrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] [AddCommGroup F] [Module 𝕜 F] | ||
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| lemma image_extremePoints (f : E ≃ₗ[𝕜] F) (s : Set E) : |
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extremePoints is not in a namespace
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I meant LinearEquiv.image_extremePoints. Or use a typeclass assumption on the type of f (LinearEquivClass?). BTW, this is true for affine equivalences as well but we don't have AffineEquivClass yet.
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Ah yeah sure. My hope was that we will only need one lemma for all of them.
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Switched to using LinearEquivClass. You can see why I originally didn't want to do that.
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We have functions "from class to hom" for some other homs. I think that we should either add it here, or generalize relevant parts to *Class. I can have a look in ~1h.
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I golfed. I think that we should add a definition SemilinearMapClass.toLinearMap but this may wait.
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Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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revert . fix a bit blech one more comment out broken and unused results chore: bump Std remove redundant simp lemmas cleanup fix: make `Nat.testBit_bitwise` a simp-lemma again. This fixes the Int.testbit_bitwise proofs fix `castNum_testBit` fix `testBit_eq_inth` fixes golf golf Apply suggestions from code review Co-authored-by: Eric Wieser <wieser.eric@gmail.com> fix whitespace fix name conflict more efficient restore lemma feat: Mapping extreme points under continuous maps (#8574) Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> chore(Profinite): allow more universe flexibility in Profinite/CofilteredLimit (#8613) We allow the indexing category for the cofiltered limit in the result `Profinite.exists_locallyConstant` to live in a smaller universe than our profinite sets. feat(CategoryTheory): `Preregular` and `FinitaryPreExtensive` implies `Precoherent` (#8643) We prove some results about effective epimorphisms which allow us to deduce that a category which is `FinitaryPreExtensive` and `Preregular` is also `Precoherent`. feat(Analysis/Seminorm): add more `*ball_smul_*ball` (#8724) We had `ball_smul_ball` and `closedBall_smul_closedBall`. Add versions with mixed `ball` and `closedBall`. Also move this lemmas below and golf the proofs. feat: the annihilator of the kernel of the trace form of a Lie module is contained in the span of its weights (#8739) fix breakage in BitVec lemmas
alexkeizer
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Nov 30, 2023
revert . fix a bit blech one more comment out broken and unused results chore: bump Std remove redundant simp lemmas cleanup fix: make `Nat.testBit_bitwise` a simp-lemma again. This fixes the Int.testbit_bitwise proofs fix `castNum_testBit` fix `testBit_eq_inth` fixes golf golf Apply suggestions from code review Co-authored-by: Eric Wieser <wieser.eric@gmail.com> fix whitespace fix name conflict more efficient restore lemma feat: Mapping extreme points under continuous maps (#8574) Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> chore(Profinite): allow more universe flexibility in Profinite/CofilteredLimit (#8613) We allow the indexing category for the cofiltered limit in the result `Profinite.exists_locallyConstant` to live in a smaller universe than our profinite sets. feat(CategoryTheory): `Preregular` and `FinitaryPreExtensive` implies `Precoherent` (#8643) We prove some results about effective epimorphisms which allow us to deduce that a category which is `FinitaryPreExtensive` and `Preregular` is also `Precoherent`. feat(Analysis/Seminorm): add more `*ball_smul_*ball` (#8724) We had `ball_smul_ball` and `closedBall_smul_closedBall`. Add versions with mixed `ball` and `closedBall`. Also move this lemmas below and golf the proofs. feat: the annihilator of the kernel of the trace form of a Lie module is contained in the span of its weights (#8739) fix breakage in BitVec lemmas
awueth
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Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme
points of the image of that set.
Also fix a few name and tweak the API a bit.