Theorems · Theorem · general topology
lipschitzOnWith_iff_restrict
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {s : Set α}
{f : α → β}, LipschitzOnWith K f s ↔ LipschitzWith K (s.domRestrict f)- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 4 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- EDist.edistproof · cited by 735
- Set.domRestrictstatement · cited by 383
- LipschitzWithstatement · cited by 316
- LipschitzOnWithstatement · cited by 164
Cited by4
Results whose statement or proof uses this declaration.
- LipschitzOnWith.to_restrictproof · cited by 5
- LipschitzWith.comp_lipschitzOnWithproof · cited by 4
- LipschitzOnWith.compproof · cited by 3
- Set.MapsTo.lipschitzOnWith_iff_restrictproof · cited by 1