Theorems · Theorem · general topology
AntilipschitzWith.isUniformEmbedding
∀ {α : Type u_4} {β : Type u_5} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
AntilipschitzWith K f → UniformContinuous f → IsUniformEmbedding f- Cited by
- 6 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.
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- UniformContinuousstatement and proof · cited by 410
- EMetricSpacestatement and proof · cited by 242
- AntilipschitzWithstatement and proof · cited by 132
- IsUniformEmbeddingstatement · cited by 107
- AntilipschitzWith.injectiveproof · cited by 8
- AntilipschitzWith.isUniformInducingproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Isometry.isUniformEmbeddingproof · cited by 4
- AntilipschitzWith.isClosedEmbeddingproof · cited by 3
- Dilation.isUniformEmbeddingproof · cited by 1
- ContinuousLinearMap.isUniformEmbedding_of_boundproof · cited by 1
- MeasureTheory.MemLp.of_comp_antilipschitzWithproof · cited by 1
- Complex.isUniformEmbedding_equivRealProdproof · cited by 0