Theorems · Theorem · general topology
Metric.hausdorffEDist_ne_top_of_nonempty_of_bounded
∀ {α : Type u} [inst : PseudoMetricSpace α] {s t : Set α},
s.Nonempty → t.Nonempty → Bornology.IsBounded s → Bornology.IsBounded t → Metric.hausdorffEDist s t ≠ ⊤If two sets are nonempty and bounded in a metric space, they are at finite Hausdorff edistance.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realproof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.Nonemptystatement and proof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- le_transproof · cited by 985
- ENNReal.ofRealproof · cited by 863
- Metric.closedBallproof · cited by 704
- Bornology.IsBoundedstatement and proof · cited by 293
- le_max_leftproof · cited by 215
Cited by4
Results whose statement or proof uses this declaration.
- ConvexBody.hausdorffEDist_ne_topproof · cited by 2
- GromovHausdorff.ghDist_le_of_approx_subsetsproof · cited by 1
- GromovHausdorff.hausdorffDist_optimalproof · cited by 1
- Metric.hausdorffEdist_ne_top_of_nonempty_of_boundedproof · cited by 0