Theorems · Theorem · general topology
Metric.hausdorffDist_comm
∀ {α : Type u} [inst : PseudoMetricSpace α] {s t : Set α}, Metric.hausdorffDist s t = Metric.hausdorffDist t sThe Hausdorff distances from s to t and from t to s coincide.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 154 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.
Cites7
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
- Metric.hausdorffDiststatement · cited by 30
- Metric.hausdorffEDist_commproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Metric.exists_dist_lt_of_hausdorffDist_lt'proof · cited by 1
- Metric.hausdorffDist_empty'proof · cited by 1
- Metric.hausdorffDist_triangle'proof · cited by 1