Theorems · Theorem · convex and discrete geometry

Convex.openSegment_interior_closure_subset_interior

∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Field 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousConstSMul 𝕜 E] {s : Set E},
  Convex 𝕜 s → ∀ {x y : E}, x ∈ interior s → y ∈ closure s → openSegment 𝕜 x y ⊆ interior s

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

5 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldPartialOrderAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul