Theorems · Theorem · convex and discrete geometry

Convex.strictConvex_of_isOpen

∀ {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 : Module 𝕜 E] {s : Set E}, IsOpen s → Convex 𝕜 s → StrictConvex 𝕜 s

An open convex set is strictly convex.

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderTopologicalSpaceAddCommMonoidModule