Theorems · Theorem · functional analysis

SemilinearIsometryClass.diam_image

∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} {𝓕 : Type u_10} [inst : Semiring R]
  [inst_1 : Semiring R₂] {σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup E₂]
  [inst_4 : Module R E] [inst_5 : Module R₂ E₂] [inst_6 : FunLike 𝓕 E E₂] [SemilinearIsometryClass 𝓕 σ₁₂ E E₂] (f : 𝓕)
  (s : Set E), Metric.diam (⇑f '' s) = Metric.diam s

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

0 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSeminormedAddCommGroupSeminormedAddCommGroupModuleModuleFunLikeSemilinearIsometryClass