Theorems · Definition · general topology
Metric.hausdorffDist
{α : Type u} → [PseudoMetricSpace α] → Set α → Set α → ℝThe Hausdorff distance between two sets is the smallest nonnegative r such that each set is
included in the r-neighborhood of the other. If there is no such r, it is defined to
be 0, arbitrarily.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 152 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.
Cites5
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 · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.toRealproof · cited by 859
- Metric.hausdorffEDistproof · cited by 76
Cited by30
Results whose statement or proof uses this declaration.
- GromovHausdorff.ghDist_le_hausdorffDiststatement and proof · cited by 3
- Metric.hausdorffDist_commstatement · cited by 3
- Metric.hausdorffDist_imagestatement · cited by 3
- Metric.hausdorffDist_le_of_mem_diststatement · cited by 3
- Metric.exists_dist_lt_of_hausdorffDist_ltstatement and proof · cited by 2
- Metric.hausdorffDist_emptystatement and proof · cited by 2
- Metric.hausdorffDist_nonnegstatement · cited by 2
- Metric.hausdorffDist_trianglestatement · cited by 2
- GromovHausdorff.ghDist_le_nonemptyCompacts_distproof · cited by 1
- GromovHausdorff.ghDist_le_of_approx_subsetsproof · cited by 1
- GromovHausdorff.hausdorffDist_optimalstatement and proof · cited by 1
- GromovHausdorff.hausdorffDist_optimal_le_HDstatement · cited by 1