Mathlib Map

Theorems · Theorem · general topology

Isometry.isUniformInducing

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  Isometry f → IsUniformInducing f

An isometry from a metric space is a uniform inducing map

Defined in
Mathlib.Topology.MetricSpace.Isometry
Cited by
10 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
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Around this declaration

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

Isometry.comp_continuous_iff · cited by 5Isometry.comp_continuous_…Topology.IsClosedEmbedding.polishSpace · cited by 2IsClosedEmbedding.polishS…Isometry.comp_continuousOn_iff · cited by 2Isometry.comp_continuousO…LinearIsometry.isComplete_image_iff · cited by 1LinearIsometry.isComplete…IsometryEquiv.completeSpace_iff · cited by 1IsometryEquiv.completeSpa…Topology.IsClosedEmbedding.IsCompletelyMetrizableSpace · cited by 1IsClosedEmbedding.IsCompl…Topology.IsClosedEmbedding.IsCompletelyPseudoMetrizableSpace · cited by 1IsClosedEmbedding.IsCompl…OrthogonalFamily.range_linearIsometry · cited by 1OrthogonalFamily.range_li…Isometry.tendsto_nhds_iff · cited by 0Isometry.tendsto_nhds_iffMetric.Sigma.completeSpace · cited by 0Sigma.completeSpacePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceIsometry · cited by 230IsometryIsUniformInducing · cited by 128IsUniformInducingIsometry.antilipschitz · cited by 14Isometry.antilipschitzAntilipschitzWith.isUniformInducing · cited by 8AntilipschitzWith.isUnifo…Isometry.uniformContinuous · cited by 3Isometry.uniformContinuousIsometry.isUniformInducingCITED BYCITES

Cites6

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Cited by10

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