Metric.mem_closure_iff_infDist_zero

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

A point belongs to the closure of s iff its infimum distance to this set vanishes.

Defined in: Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by: 5 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace

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