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Theorems · Definition · general topology

PiCountable.pseudoEMetricSpace

{ι : Type u_2} →
  [Encodable ι] → {F : ι → Type u_3} → [(i : ι) → PseudoEMetricSpace (F i)] → PseudoEMetricSpace ((i : ι) → F i)

Given a countable family of extended pseudometric spaces, one may put an extended distance on their product Π i, E i. It is highly non-canonical, though, and therefore not registered as a global instance. The distance we use here is edist x y = ∑' i, min (1/2)^(encode i) (edist (x i) (y i)).

Defined in
Mathlib.Topology.MetricSpace.PiNat
Cited by
1 results in Mathlib
Foundations
Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
EncodablePseudoEMetricSpace
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Metric.PiNatEmbed.isometry_embed · cited by 1PiNatEmbed.isometry_embedPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEncodable · cited by 140EncodablePiCountable.pseudoEMetricSpaceCITED BYCITES

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