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Theorems · Definition · general topology

PseudoMetricSpace.replaceDist

{X : Type u_2} → (m : PseudoMetricSpace X) → (d : X → X → ℝ) → d = dist → PseudoMetricSpace X

Build new pseudometric space from an old one where the distance is provably (but typically non-definitionally) equal to some given distance. We also provide convenience versions for PseudoEMetric, Emetric and Metric spaces.

Defined in
Mathlib.Topology.MetricSpace.Basic
Cited by
1 results in Mathlib
Foundations
Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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PseudoMetricSpace.replaceDist_eq · cited by 0PseudoMetricSpace.replace…Real · cited by 25697RealPseudoMetricSpace · cited by 1550PseudoMetricSpaceDist.dist · cited by 1539Dist.distPseudoMetricSpace.edist · cited by 1PseudoMetricSpace.edistPseudoMetricSpace.replaceDistCITED BYCITES

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