Theorems · Theorem · convex and discrete geometry

strictConvex_iff_convex

∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
  [OrderTopology 𝕜] {s : Set 𝕜}, StrictConvex 𝕜 s ↔ Convex 𝕜 s

A set in a linear ordered field is strictly convex if and only if it is convex.

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingTopologicalSpaceOrderTopology