Mathlib Map

Theorems · Definition · general topology

TopologicalSpace.NonemptyCompacts.toGHSpace

{X : Type u} → [inst : MetricSpace X] → TopologicalSpace.NonemptyCompacts X → GromovHausdorff.GHSpace

In particular, nonempty compacts of a metric space map to GHSpace. We register this in the TopologicalSpace namespace to take advantage of the notation p.toGHSpace.

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
MetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

GromovHausdorff.ghDist_le_nonemptyCompacts_dist · cited by 1GromovHausdorff.ghDist_le…GromovHausdorff.toGHSpace_lipschitz · cited by 1GromovHausdorff.toGHSpace…GromovHausdorff.toGHSpace_continuous · cited by 0GromovHausdorff.toGHSpace…MetricSpace · cited by 1684MetricSpaceTopologicalSpace.NonemptyCompacts · cited by 137TopologicalSpace.Nonempty…GromovHausdorff.GHSpace · cited by 8GromovHausdorff.GHSpaceGromovHausdorff.toGHSpace · cited by 8GromovHausdorff.toGHSpaceNonemptyCompacts.toGHSpaceCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.