Theorems · Theorem · general topology
Isometry.isUniformEmbedding
∀ {α : Type u} {β : Type v} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → IsUniformEmbedding fAn isometry from an emetric space is a uniform embedding
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 4 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EMetricSpacestatement and proof · cited by 242
- Isometrystatement and proof · cited by 230
- IsUniformEmbeddingstatement · cited by 107
- LipschitzWith.uniformContinuousproof · cited by 33
- Isometry.lipschitzproof · cited by 22
- Isometry.antilipschitzproof · cited by 14
- AntilipschitzWith.isUniformEmbeddingproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Isometry.isEmbeddingproof · cited by 4
- Metric.PiNatEmbed.isUniformEmbedding_embedproof · cited by 2
- RCLike.isUniformEmbedding_ofRealproof · cited by 1
- Complex.isUniformEmbedding_ofRealproof · cited by 1