Theorems · Theorem · convex and discrete geometry

strictConvex_iff_openSegment_subset

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : AddCommMonoid E] [inst_4 : SMul 𝕜 E] {s : Set E},
  StrictConvex 𝕜 s ↔ s.Pairwise fun x y => openSegment 𝕜 x y ⊆ interior s

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

3 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

SemiringPartialOrderTopologicalSpaceAddCommMonoidSMul