Theorems · Theorem · general topology

Topology.IsEmbedding.to_isometry

∀ {α : Type u_3} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β}
  (h : Topology.IsEmbedding f), Isometry f

An embedding from a topological space to a pseudometric space is an isometry with respect to the induced pseudometric space structure on the source space.

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

3 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpace