Theorems · Theorem · general topology
LipschitzOnWith.uniformContinuousOn
∀ {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 → UniformContinuousOn f s- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 2 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.
Cites8
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
- LipschitzOnWithstatement and proof · cited by 164
- UniformContinuousOnstatement · cited by 47
- LipschitzWith.uniformContinuousproof · cited by 33
- uniformContinuousOn_iff_restrictproof · cited by 8
- LipschitzOnWith.to_restrictproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzOnWith.continuousOnproof · cited by 1
- LipschitzOnWith.uniformEquicontinuousOnproof · cited by 0