Mathlib Map

Theorems · Definition · functional analysis

NormedAddGroupHom.ofLipschitz

{V₁ : Type u_2} →
  {V₂ : Type u_3} →
    [inst : SeminormedAddCommGroup V₁] →
      [inst_1 : SeminormedAddCommGroup V₂] →
        (f : V₁ →+ V₂) → {K : NNReal} → LipschitzWith K ⇑f → NormedAddGroupHom V₁ V₂

A Lipschitz continuous additive homomorphism is a normed additive group homomorphism.

Defined in
Mathlib.Analysis.Normed.Group.Hom
Cited by
1 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupSeminormedAddCommGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NormedAddGroupHom.completion · cited by 15NormedAddGroupHom.complet…NormedAddGroupHom.extension · cited by 4NormedAddGroupHom.extensi…NormedAddGroupHom.ofLipschitz_norm_le · cited by 1NormedAddGroupHom.ofLipsc…DFunLike.coe · cited by 62936DFunLike.coeNNReal · cited by 4310NNRealAddMonoidHom · cited by 3230AddMonoidHomSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNNReal.toReal · cited by 1260NNReal.toRealLipschitzWith · cited by 316LipschitzWithNormedAddGroupHom · cited by 216NormedAddGroupHomAddMonoidHom.mkNormedAddGroupHom · cited by 5AddMonoidHom.mkNormedAddG…NormedAddGroupHom.ofLipschitzCITED BYCITES

Cites8

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Cited by3

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