Metric.mem_thickening_iff

∀ {δ : ℝ} {X : Type u} [inst : PseudoMetricSpace X] {E : Set X} {x : X},
  x ∈ Metric.thickening δ E ↔ ∃ z ∈ E, dist x z < δ

A point in a metric space belongs to the (open) δ-thickening of a subset E if and only if it is at distance less than δ from some point of E.

Defined in: Mathlib.Topology.MetricSpace.Thickening
Cited by: 6 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace

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