Theorems · Theorem · convex and discrete geometry

StrictConvex.linearIsometry_preimage

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedField 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] [inst_4 : SeminormedAddCommGroup F]
  [inst_5 : NormedSpace 𝕜 F] {s : Set F}, StrictConvex 𝕜 s → ∀ (e : E →ₗᵢ[𝕜] F), StrictConvex 𝕜 (⇑e ⁻¹' s)

Defined in

Mathlib.Analysis.Convex.LinearIsometry

Cited by

1 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldPartialOrderNormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace