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Theorems · Theorem · general topology

Metric.hausdorffDist_nonneg

∀ {α : Type u} [inst : PseudoMetricSpace α] {s t : Set α}, 0 ≤ Metric.hausdorffDist s t

The Hausdorff distance is nonnegative.

Defined in
Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by
2 results in Mathlib
Foundations
Depth 153 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.

GromovHausdorff.ghDist_le_hausdorffDist · cited by 3GromovHausdorff.ghDist_le…Metric.exists_dist_lt_of_hausdorffDist_lt · cited by 2Metric.exists_dist_lt_of_…Set · cited by 53352SetReal · cited by 25697RealPseudoMetricSpace · cited by 1550PseudoMetricSpaceMetric.hausdorffDist · cited by 30Metric.hausdorffDistMetric.hausdorffDist_nonnegCITED BYCITES

Cites4

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Cited by2

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