Theorems · Theorem · convex and discrete geometry

StrictConvex.preimage_smul

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : CommSemiring 𝕜] [IsDomain 𝕜] [inst_2 : PartialOrder 𝕜]
  [inst_3 : TopologicalSpace E] [inst_4 : AddCommGroup E] [inst_5 : Module 𝕜 E] [Module.IsTorsionFree 𝕜 E]
  [ContinuousConstSMul 𝕜 E] {s : Set E}, StrictConvex 𝕜 s → ∀ (c : 𝕜), StrictConvex 𝕜 ((fun z => c • z) ⁻¹' s)

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringIsDomainPartialOrderTopologicalSpaceAddCommGroupModuleModule.IsTorsionFreeContinuousConstSMul