Theorems · Theorem · functional analysis

ContinuousLinearMap.closed_range_of_antilipschitz

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜'] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {σ : 𝕜 →+* 𝕜'} {σ' : 𝕜' →+* 𝕜}
  [inst_4 : RingHomInvPair σ σ'] {F : Type u_4} [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜' F]
  [CompleteSpace E] {f : E →SL[σ] F} {c : NNReal}, AntilipschitzWith c ⇑f → (↑f).range.topologicalClosure = (↑f).range

Defined in

Mathlib.Analysis.Normed.Operator.Banach

Cited by

1 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAddCommGroupNormedSpaceRingHomInvPairNormedAddCommGroupNormedSpaceCompleteSpace