Theorems · Theorem · convex and discrete geometry

StrictConvex.vadd

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] [ContinuousAdd E] {s : Set E},
  StrictConvex 𝕜 s → ∀ (x : E), StrictConvex 𝕜 (x +ᵥ s)

The translation of a strictly convex set is also strictly convex.

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringPartialOrderTopologicalSpaceAddCommGroupModuleContinuousAdd