Theorems · Theorem · convex and discrete geometry

Set.OrdConnected.strictConvex

∀ {𝕜 : Type u_1} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace β]
  [inst_3 : AddCommMonoid β] [inst_4 : LinearOrder β] [IsOrderedCancelAddMonoid β] [OrderTopology β]
  [inst_7 : Module 𝕜 β] [PosSMulStrictMono 𝕜 β] {s : Set β}, s.OrdConnected → StrictConvex 𝕜 s

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

9 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderTopologicalSpaceAddCommMonoidLinearOrderIsOrderedCancelAddMonoidOrderTopologyModulePosSMulStrictMono