Theorems · Theorem · general topology
LipschitzOnWith.continuousOn
∀ {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 → ContinuousOn f s- 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
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ContinuousOnstatement · cited by 1,411
- LipschitzOnWithstatement and proof · cited by 164
- UniformContinuousOn.continuousOnproof · cited by 3
- LipschitzOnWith.uniformContinuousOnproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LocallyLipschitz.continuousproof · cited by 2