Totally_Bounded_Metric_Space_is_Separable
Provedmetric-spacesproofwikiseparable-spacestotally-bounded-metric-spaces
A totally bounded metric space is separable.
Preamble
import Mathlib.Topology.MetricSpace.Basic
Formal statement
theorem Totally_Bounded_Metric_Space_is_Separable {α : Type _} [PseudoMetricSpace α] (h : TotallyBounded (Set.univ : Set α)) : ∃ (s : Set α), s.Countable ∧ Dense s := by sorrySource