Theorems · Theorem · general topology
Metric.hausdorffEDist_closure_right
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
Metric.hausdorffEDist s (closure t) = Metric.hausdorffEDist s tReplacing a set by its closure does not change the Hausdorff edistance.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- closurestatement and proof · cited by 1,254
- Metric.hausdorffEDiststatement and proof · cited by 76
- Metric.hausdorffEDist_commproof · cited by 11
- Metric.hausdorffEDist_closure_leftproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Metric.hausdorffEDist_closureproof · cited by 1
- Metric.hausdorffDist_closure₂proof · cited by 0
- Metric.hausdorffDist_closureproof · cited by 0
- EMetric.hausdorffEdist_closure₂proof · cited by 0