Theorems · Theorem · convex and discrete geometry

StrictConvex.affine_image

∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : TopologicalSpace F] [inst_4 : AddCommGroup E] [inst_5 : AddCommGroup F] [inst_6 : Module 𝕜 E]
  [inst_7 : Module 𝕜 F] {s : Set E}, StrictConvex 𝕜 s → ∀ {f : E →ᵃ[𝕜] F}, IsOpenMap ⇑f → StrictConvex 𝕜 (⇑f '' s)

The image of a strictly convex set under an affine map is strictly convex.

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderTopologicalSpaceTopologicalSpaceAddCommGroupAddCommGroupModuleModule