Theorems · Theorem · general topology
Metric.hausdorffDist_closure
∀ {α : Type u} [inst : PseudoMetricSpace α] {s t : Set α},
Metric.hausdorffDist (closure s) (closure t) = Metric.hausdorffDist s tThe Hausdorff distances between two sets and their closures coincide.
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- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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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
- closurestatement · cited by 1,254
- ENNReal.toRealproof · cited by 859
- Metric.hausdorffEDistproof · cited by 76
- Metric.hausdorffDiststatement · cited by 30
- Metric.hausdorffEDist_closure_leftproof · cited by 5
- Metric.hausdorffEDist_closure_rightproof · cited by 4
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