Theorems · Theorem · general topology

Metric.hausdorffDist_empty

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

The Hausdorff distance to the empty set vanishes (if you want to have the more reasonable value ∞ instead, use Metric.hausdorffEDist, which takes values in ℝ≥0∞).

Defined in

Mathlib.Topology.MetricSpace.HausdorffDistance

Cited by

2 results in Mathlib

Foundations

Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace