Theorems · Theorem · general topology
Metric.hausdorffDist_le_of_infDist
∀ {α : Type u} [inst : PseudoMetricSpace α] {s t : Set α} {r : ℝ},
0 ≤ r → (∀ x ∈ s, Metric.infDist x t ≤ r) → (∀ x ∈ t, Metric.infDist x s ≤ r) → Metric.hausdorffDist s t ≤ rBounding the Hausdorff distance by bounding the distance of any point in each set to the other set
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 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.
Cites15
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
- Realstatement and proof · cited by 25,697
- Set.Nonemptyproof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.ofRealproof · cited by 863
- Set.eq_empty_or_nonemptyproof · cited by 248
- Metric.hausdorffEDistproof · cited by 76
- Metric.infDiststatement and proof · cited by 68
- Metric.hausdorffDiststatement · cited by 30
- ENNReal.toReal_le_of_le_ofRealproof · cited by 14
- ENNReal.le_ofReal_iff_toReal_leproof · cited by 11
- Metric.infEDist_ne_topproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Metric.hausdorffDist_le_of_mem_distproof · cited by 3