Theorems · Theorem · convex and discrete geometry

mem_exposedPoints_iff_exposed_singleton

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace 𝕜] [inst_1 : Ring 𝕜] [inst_2 : PartialOrder 𝕜]
  [inst_3 : AddCommMonoid E] [inst_4 : TopologicalSpace E] [inst_5 : Module 𝕜 E] {A : Set E} {x : E},
  x ∈ Set.exposedPoints 𝕜 A ↔ IsExposed 𝕜 A {x}

Exposed points exactly correspond to exposed singletons.

Defined in

Mathlib.Analysis.Convex.Exposed

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceRingPartialOrderAddCommMonoidTopologicalSpaceModule