Theorems · Theorem · convex and discrete geometry

AmpleSet.image_iff

∀ {F : Type u_1} [inst : AddCommGroup F] [inst_1 : Module ℝ F] [inst_2 : TopologicalSpace F] {E : Type u_2}
  [inst_3 : AddCommGroup E] [inst_4 : Module ℝ E] [inst_5 : TopologicalSpace E] {s : Set E} (L : E ≃ᴬ[ℝ] F),
  AmpleSet (⇑L '' s) ↔ AmpleSet s

A set is ample iff its image under a continuous affine equivalence is.

Defined in

Mathlib.Analysis.Convex.AmpleSet

Cited by

1 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace