IsClosed.mem_iff_infDist_zero

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α},
  IsClosed s → s.Nonempty → (x ∈ s ↔ Metric.infDist x s = 0)

Given a closed set s, a point belongs to s iff its infimum distance to this set vanishes

Defined in: Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by: 3 results in Mathlib
Foundations: Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace

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