Theorems · Theorem · general topology

GromovHausdorff.eq_toGHSpace_iff

∀ {X : Type u} [inst : MetricSpace X] [inst_1 : CompactSpace X] [inst_2 : Nonempty X]
  {p : TopologicalSpace.NonemptyCompacts ↥(lp (fun n => ℝ) ⊤)},
  ⟦p⟧ = GromovHausdorff.toGHSpace X ↔ ∃ Ψ, Isometry Ψ ∧ Set.range Ψ = ↑p

Defined in

Mathlib.Topology.MetricSpace.GromovHausdorff

Cited by

3 results in Mathlib

Foundations

Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MetricSpaceCompactSpaceNonempty