Theorems · Theorem · general topology
lipschitzOnWith_univ
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
LipschitzOnWith K f Set.univ ↔ LipschitzWith K ff is Lipschitz iff it is Lipschitz on the entire space.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- Set.univstatement · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- EDist.edistproof · cited by 735
- LipschitzWithstatement · cited by 316
- LipschitzOnWithstatement · cited by 164
Cited by11
Results whose statement or proof uses this declaration.
- LipschitzWith.locallyLipschitzproof · cited by 6
- lipschitzWith_of_nnnorm_deriv_leproof · cited by 4
- LipschitzWith.addproof · cited by 3
- norm_fderiv_le_of_lipschitzproof · cited by 2
- norm_lineDeriv_le_of_lipschitzproof · cited by 1
- lipschitzWith_of_nnnorm_fderiv_leproof · cited by 1
- holderWith_oneproof · cited by 1
- HasFDerivAt.le_of_lipschitzproof · cited by 1
- LipschitzWith.ae_differentiableAtproof · cited by 1
- HasLineDerivAt.le_of_lipschitzproof · cited by 0
- ApproximatesLinearOn.exists_homeomorph_extensionproof · cited by 0