Theorems · Theorem · general topology
LipschitzWith.uniformContinuous
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f → UniformContinuous fA Lipschitz function is uniformly continuous.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 33 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealproof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- ne_of_gtproof · cited by 637
- UniformContinuousstatement · cited by 410
- LipschitzWithstatement and proof · cited by 316
- ENNReal.coe_ne_topproof · cited by 100
- ENNReal.div_pos_iffproof · cited by 7
- EMetric.uniformContinuous_iffproof · cited by 3
- LipschitzWith.edist_lt_of_edist_lt_divproof · cited by 2
Cited by33
Results whose statement or proof uses this declaration.
- LipschitzWith.continuousproof · cited by 30
- Isometry.isClosedEmbeddingproof · cited by 15
- NumberField.InfinitePlace.mk_eq_iffproof · cited by 5
- Isometry.isUniformEmbeddingproof · cited by 4
- uniformContinuous_normproof · cited by 4
- NormedAddGroupHom.uniformContinuousproof · cited by 4
- LipschitzWith.memLp_comp_iff_of_antilipschitzproof · cited by 3
- Isometry.uniformContinuousproof · cited by 3
- Dilation.isUniformInducingproof · cited by 3
- LipschitzOnWith.uniformContinuousOnproof · cited by 2
- uniformContinuous_norm'proof · cited by 1
- BoundedContinuousFunction.uniformContinuous_coeproof · cited by 1