Theorems · Theorem · functional analysis

DilationEquiv.smulTorsor_preimage_ball

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : NormSMulClass 𝕜 E] {P : Type u_3} [inst_4 : PseudoMetricSpace P] [inst_5 : NormedAddTorsor E P] {c : P}
  {k : 𝕜} (hk : k ≠ 0), ⇑(DilationEquiv.smulTorsor c hk) ⁻¹' Metric.ball c ‖k‖ = Metric.ball 0 1

Defined in

Mathlib.Analysis.Normed.Affine.AddTorsor

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedDivisionRingSeminormedAddCommGroupModuleNormSMulClassPseudoMetricSpaceNormedAddTorsor