Theorems · Theorem · general topology
LocallyLipschitzOn.restrict
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {s : Set α} {f : α → β},
LocallyLipschitzOn s f → LocallyLipschitz (s.domRestrict f)Alias of the forward direction of locallyLipschitzOn_iff_restrict.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.domRestrictstatement · cited by 383
- LocallyLipschitzstatement · cited by 34
- LocallyLipschitzOnstatement · cited by 29
- locallyLipschitzOn_iff_restrictproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LocallyLipschitzOn.continuousOnproof · cited by 6