Theorems · Theorem · convex and discrete geometry

isExtreme_singleton

∀ {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} {x : E}, IsExtreme 𝕜 A {x} ↔ x ∈ Set.extremePoints 𝕜 A

x is an extreme point to A iff {x} is an extreme set of A.

Defined in

Mathlib.Analysis.Convex.Extreme

Cited by

2 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidSMul