Theorems · Theorem · convex and discrete geometry

StrictConvex.linear_preimage

∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : TopologicalSpace E] [inst_3 : TopologicalSpace F] [inst_4 : AddCommMonoid E] [inst_5 : AddCommMonoid F]
  [inst_6 : Module 𝕜 E] [inst_7 : Module 𝕜 F] {s : Set F},
  StrictConvex 𝕜 s → ∀ (f : E →ₗ[𝕜] F), Continuous ⇑f → Function.Injective ⇑f → StrictConvex 𝕜 (⇑f ⁻¹' s)

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

4 results in Mathlib

Foundations

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

Assumes

SemiringPartialOrderTopologicalSpaceTopologicalSpaceAddCommMonoidAddCommMonoidModuleModule