Theorems · Theorem · convex and discrete geometry
extremePoints_subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : SMul 𝕜 E] {A : Set E}, Set.extremePoints 𝕜 A ⊆ A- Defined in
- Mathlib.Analysis.Convex.Extreme
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.extremePointsstatement and proof · cited by 43
Cited by8
Results whose statement or proof uses this declaration.
- StrictConvex.extremePoints_eq_sdiff_interiorproof · cited by 2
- closure_convexHull_extremePointsproof · cited by 0
- Set.extremePoints_eq_selfproof · cited by 0
- extremePoints_closedBall_subset_sphereproof · cited by 0
- surjOn_extremePoints_imageproof · cited by 0
- extremePoints_emptyproof · cited by 0
- Convex.convexIndependent_extremePointsproof · cited by 0
- extremePoints_singletonproof · cited by 0