Theorems · Theorem · convex and discrete geometry

StrictConvex.eq_of_openSegment_subset_frontier

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {s : Set E} {x y : E} [IsOrderedRing 𝕜] [Nontrivial 𝕜]
  [DenselyOrdered 𝕜], StrictConvex 𝕜 s → x ∈ s → y ∈ s → openSegment 𝕜 x y ⊆ frontier s → x = y

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

0 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderTopologicalSpaceAddCommGroupModuleIsOrderedRingNontrivialDenselyOrdered