Theorems · Theorem · general topology
locallyLipschitzOn_iff_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)- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- 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.
Cites19
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
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- NNRealproof · cited by 4,310
- LE.le.transproof · cited by 3,151
- nhdsWithinproof · cited by 1,912
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.domRestrictstatement · cited by 383
- Set.inter_subset_rightproof · cited by 329
- Set.Subset.rflproof · cited by 255
- self_mem_nhdsWithinproof · cited by 215
Cited by1
Results whose statement or proof uses this declaration.
- LocallyLipschitzOn.restrictproof · cited by 1