Theorems · Theorem · functional analysis
NormedAddGroupHom.lipschitz
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂), LipschitzWith ⟨‖f‖, ⋯⟩ ⇑fcontinuous linear maps are Lipschitz continuous.
- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.distproof · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- map_subproof · cited by 565
- LipschitzWithstatement · cited by 316
- NormedAddGroupHomstatement and proof · cited by 216
- dist_eq_normproof · cited by 182
- LipschitzWith.of_dist_le_mulproof · cited by 13
- NormedAddGroupHom.le_opNormproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.uniformContinuousproof · cited by 4