Theorems · Theorem · convex and discrete geometry

StrictConvex.is_linear_image

∀ {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 E},
  StrictConvex 𝕜 s → ∀ {f : E → F}, IsLinearMap 𝕜 f → IsOpenMap f → StrictConvex 𝕜 (f '' 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

SemiringPartialOrderTopologicalSpaceTopologicalSpaceAddCommMonoidAddCommMonoidModuleModule