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Theorems · Theorem · general topology

GromovHausdorff.isometry_optimalGHInjl

∀ (X : Type u) (Y : Type v) [inst : MetricSpace X] [inst_1 : CompactSpace X] [inst_2 : Nonempty X]
  [inst_3 : MetricSpace Y] [inst_4 : CompactSpace Y] [inst_5 : Nonempty Y], Isometry (GromovHausdorff.optimalGHInjl X Y)

The injection of X in the optimal coupling between X and Y is an isometry.

Defined in
Mathlib.Topology.MetricSpace.GromovHausdorffRealized
Cited by
2 results in Mathlib
Foundations
Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MetricSpaceCompactSpaceNonemptyMetricSpaceCompactSpaceNonempty
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GromovHausdorff.hausdorffDist_optimal · cited by 1GromovHausdorff.hausdorff…GromovHausdorff.ghDist_eq_hausdorffDist · cited by 0GromovHausdorff.ghDist_eq…MetricSpace · cited by 1684MetricSpaceCompactSpace · cited by 593CompactSpaceIsometry · cited by 230IsometryIsometry.of_dist_eq · cited by 27Isometry.of_dist_eqGromovHausdorff.OptimalGHCoupling · cited by 5GromovHausdorff.OptimalGH…GromovHausdorff.optimalGHInjl · cited by 4GromovHausdorff.optimalGH…GromovHausdorff.isometry_opti…CITED BYCITES

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