Theorems · Theorem · general topology

GromovHausdorff.HD_candidatesBDist_le

∀ {X : Type u} {Y : Type v} [inst : MetricSpace X] [inst_1 : MetricSpace Y] [inst_2 : CompactSpace X]
  [inst_3 : CompactSpace Y] [inst_4 : Nonempty X] [inst_5 : Nonempty Y],
  GromovHausdorff.HD (GromovHausdorff.candidatesBDist X Y) ≤ Metric.diam Set.univ + 1 + Metric.diam Set.univ

Explicit bound on HD (dist). This means that when looking for minimizers it will be sufficient to look for functions with HD(f) bounded by this bound.

Defined in: Mathlib.Topology.MetricSpace.GromovHausdorffRealized
Cited by: 1 results in Mathlib
Foundations: Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MetricSpace MetricSpace CompactSpace CompactSpace Nonempty Nonempty

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DFunLike.coeproof · cited by 62,936
Realstatement · cited by 25,697
Set.rangeproof · cited by 4,705
Set.univstatement and proof · cited by 3,945
add_zeroproof · cited by 2,707
le_reflproof · cited by 2,061
iInfproof · cited by 1,690
MetricSpacestatement and proof · cited by 1,684
Dist.distproof · cited by 1,539
le_transproof · cited by 985
add_le_addproof · cited by 666
CompactSpacestatement and proof · cited by 593

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GromovHausdorff.hausdorffDist_optimalproof · cited by 1