Theorems · Theorem · convex and discrete geometry
StrictConvex.sdiff_interior_subset_extremePoints
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid A]
[inst_3 : Module 𝕜 A] [inst_4 : TopologicalSpace A] {C : Set A},
StrictConvex 𝕜 C → C \ interior C ⊆ Set.extremePoints 𝕜 C- Defined in
- Mathlib.Analysis.Convex.Strict.Extreme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- one_smulproof · cited by 1,374
- interiorstatement and proof · cited by 714
- add_smulproof · cited by 204
- openSegmentproof · cited by 102
- StrictConvexstatement and proof · cited by 71
- Set.extremePointsstatement · cited by 43
Cited by3
Results whose statement or proof uses this declaration.
- StrictConvex.extremePoints_eq_sdiff_interiorproof · cited by 2
- StrictConvexSpace.sphere_subset_extremePoints_closedBallproof · cited by 0
- StrictConvex.diff_interior_subset_extremePointsproof · cited by 0