Metric.exists_mem_closure_infDist_eq_dist

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} [ProperSpace α],
  s.Nonempty → ∀ (x : α), ∃ y ∈ closure s, Metric.infDist x s = dist x y

Defined in: Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by: 1 results in Mathlib
Foundations: Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace ProperSpace

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