Theorems · Theorem · general topology
IsUniformEmbedding.to_isometry
∀ {α : Type u_3} {β : Type u_4} [inst : UniformSpace α] [inst_1 : MetricSpace β] {f : α → β} (h : IsUniformEmbedding f),
Isometry fA uniform embedding from a uniform space to a metric space is an isometry with respect to the induced metric space structure on the source space.
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceMetricSpace
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- MetricSpacestatement and proof · cited by 1,684
- Isometrystatement · cited by 230
- IsUniformEmbeddingstatement and proof · cited by 107
- Isometry.of_dist_eqproof · cited by 27
- IsUniformEmbedding.comapMetricSpacestatement and proof · cited by 1
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