Theorems · Theorem · convex and discrete geometry

StrictConvex.smul

∀ {𝕜 : Type u_1} {𝕝 : Type u_2} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : TopologicalSpace E] [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] [inst_5 : Field 𝕝] [inst_6 : Module 𝕝 E]
  [ContinuousConstSMul 𝕝 E] [LinearMap.CompatibleSMul E E 𝕜 𝕝] {s : Set E},
  StrictConvex 𝕜 s → ∀ (c : 𝕝), StrictConvex 𝕜 (c • s)

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringPartialOrderTopologicalSpaceAddCommGroupModuleFieldModuleContinuousConstSMulLinearMap.CompatibleSMul