Theorems · Theorem · general topology
Metric.infEDist_closure
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s : Set α}, Metric.infEDist x (closure s) = Metric.infEDist x sThe edist to a set and to its closure coincide
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 149 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.
Cites24
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 and proof · cited by 9,879
- Top.topproof · cited by 9,680
- NNRealproof · cited by 4,310
- le_antisymmproof · cited by 2,068
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LT.lt.ne'proof · cited by 1,417
- ENNReal.ofNNRealproof · cited by 1,279
- closurestatement and proof · cited by 1,254
- le_of_ltproof · cited by 1,175
- LT.lt.neproof · cited by 872
- add_assocproof · cited by 746
Cited by8
Results whose statement or proof uses this declaration.
- Metric.mem_closure_iff_infEDist_zeroproof · cited by 3
- Metric.infDist_closureproof · cited by 2
- Metric.cthickening_closureproof · cited by 2
- infEDist_cthickeningproof · cited by 2
- Metric.thickening_closureproof · cited by 1
- Metric.infEDist_closure_pos_iff_notMem_closureproof · cited by 1
- thickenedIndicatorAux_closure_eqproof · cited by 1
- EMetric.infEdist_closureproof · cited by 0