Theorems · Theorem · general topology
Metric.infEDist_lt_iff
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s : Set α} {r : ENNReal},
Metric.infEDist x s < r ↔ ∃ y ∈ s, edist x y < rThe edist to a set is < r iff there exists a point in the set at edistance < r
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 148 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.
Cites5
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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- Metric.infEDiststatement · cited by 147
Cited by9
Results whose statement or proof uses this declaration.
- Metric.infEDist_closureproof · cited by 8
- Metric.infEDist_le_infEDist_add_hausdorffEDistproof · cited by 4
- Metric.exists_edist_lt_of_hausdorffEDist_ltproof · cited by 3
- Metric.mem_closure_iff_infEDist_zeroproof · cited by 3
- infEDist_thickeningproof · cited by 3
- Metric.ediam_cthickening_leproof · cited by 2
- MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodoryproof · cited by 1
- Metric.mem_thickening_iff_exists_edist_ltproof · cited by 1
- EMetric.infEdist_lt_iffproof · cited by 0