Theorems · Theorem · general topology
Metric.hausdorffEDist_closure_left
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
Metric.hausdorffEDist (closure s) t = Metric.hausdorffEDist s tReplacing a set by its closure does not change the Hausdorff edistance.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 157 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.
Cites10
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
- zero_addproof · cited by 2,366
- le_antisymmproof · cited by 2,068
- 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_self_closureproof · cited by 3
- Metric.hausdorffEDist_triangleproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Metric.hausdorffEDist_closure_rightproof · cited by 4
- Metric.hausdorffEDist_closureproof · cited by 1
- EMetric.hausdorffEdist_closure₁proof · cited by 0
- Metric.hausdorffDist_closureproof · cited by 0
- Metric.hausdorffDist_closure₁proof · cited by 0