Theorems · Theorem · general topology
LipschitzWith.locallyLipschitz
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β} {K : NNReal},
LipschitzWith K f → LocallyLipschitz fA Lipschitz function is locally Lipschitz.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 149 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.univproof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LipschitzWithstatement and proof · cited by 316
- Filter.univ_memproof · cited by 96
- LocallyLipschitzstatement · cited by 34
- lipschitzOnWith_univproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- LocallyLipschitz.constproof · cited by 2
- LocallyLipschitz.maxproof · cited by 1
- LocallyLipschitz.minproof · cited by 1
- LocallyLipschitz.prodMk_leftproof · cited by 0
- LocallyLipschitz.prodMk_rightproof · cited by 0
- LocallyLipschitz.idproof · cited by 0