Metric.totallyBounded_of_finite_discretization

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α},
  (∀ ε > 0, ∃ β x F, ∀ (x y : ↑s), F x = F y → dist ↑x ↑y < ε) → TotallyBounded s

A pseudometric space is totally bounded if one can reconstruct up to any ε>0 any element of the space from finitely many data.

Defined in: Mathlib.Topology.MetricSpace.Pseudo.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace

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