Theorems · Theorem · general topology

Metric.infDist_empty

∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α}, Metric.infDist x ∅ = 0

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

Defined in

Mathlib.Topology.MetricSpace.HausdorffDistance

Cited by

1 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace