Theorems · Theorem · convex and discrete geometry

StrictConvex.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} {x y : E},
  StrictConvex 𝕜 s → x ∈ s → y ∈ s → x ≠ y → openSegment 𝕜 x y ⊆ interior s

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses no axioms

Assumes

SemiringPartialOrderTopologicalSpaceAddCommMonoidSMul