Mathlib Map

Theorems · Definition · general topology

UniformSpace.pseudoMetricSpace

(X : Type u_2) → [inst : UniformSpace X] → [(uniformity X).IsCountablyGenerated] → PseudoMetricSpace X

A PseudoMetricSpace instance compatible with a given UniformSpace structure.

Defined in
Mathlib.Topology.Metrizable.Uniformity
Cited by
0 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceFilter.IsCountablyGenerated
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

TopologicalSpace.pseudoMetrizableSpacePseudoMetric · cited by 14TopologicalSpace.pseudoMe…UniformSpace · cited by 2040UniformSpacePseudoMetricSpace · cited by 1550PseudoMetricSpaceuniformity · cited by 765uniformityFilter.IsCountablyGenerated · cited by 220Filter.IsCountablyGenerat…PseudoMetricSpace.replaceUniformity · cited by 1PseudoMetricSpace.replace…UniformSpace.metrizable_uniformity · cited by 0UniformSpace.metrizable_u…UniformSpace.pseudoMetricSpaceCITED BYCITES

Cites6

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Cited by1

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