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Theorems · Theorem · general topology

Isometry.isEmbedding

∀ {α : Type u} {β : Type v} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  Isometry f → Topology.IsEmbedding f

An isometry from an emetric space is an embedding

Defined in
Mathlib.Topology.MetricSpace.Isometry
Cited by
4 results in Mathlib
Foundations
Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
EMetricSpacePseudoEMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Bornology.IsVonNBounded.image · cited by 5IsVonNBounded.imageRCLike.nonUnitalContinuousFunctionalCalculus · cited by 2RCLike.nonUnitalContinuou…LinearIsometry.isEmbedding · cited by 1LinearIsometry.isEmbeddingTopologicalSpace.exists_isInducing_l_infty · cited by 1TopologicalSpace.exists_i…PseudoEMetricSpace · cited by 1536PseudoEMetricSpaceTopology.IsEmbedding · cited by 294Topology.IsEmbeddingEMetricSpace · cited by 242EMetricSpaceIsometry · cited by 230IsometryIsUniformEmbedding.isEmbedding · cited by 25IsUniformEmbedding.isEmbe…Isometry.isUniformEmbedding · cited by 4Isometry.isUniformEmbeddi…Isometry.isEmbeddingCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.