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Theorems · Theorem · general topology

Metric.infEDist_eq_top_iff

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α}, Metric.infEDist x s = ⊤ ↔ s = ∅
Defined in
Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by
2 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpace
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Around this declaration

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

Metric.infDist_le_infDist_add_hausdorffDist · cited by 1Metric.infDist_le_infDist…Metric.infEdist_eq_top_iff · cited by 0Metric.infEdist_eq_top_iffSet · cited by 53352SetENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topSet.Nonempty · cited by 2627Set.NonemptyPseudoMetricSpace · cited by 1550PseudoMetricSpaceSet.eq_empty_or_nonempty · cited by 248Set.eq_empty_or_nonemptyMetric.infEDist · cited by 147Metric.infEDistMetric.infEDist_empty · cited by 6Metric.infEDist_emptyMetric.infEDist_eq_top_iffCITED BYCITES

Cites8

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Cited by2

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