Theorems · Theorem · general topology
Metric.IsCover.singleton_of_ediam_le
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ε : NNReal} {s : Set X} {x : X},
Metric.ediam s ≤ ↑ε → x ∈ s → Metric.IsCover ε s {x}- Defined in
- Mathlib.Topology.MetricSpace.Cover
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 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.
Cites9
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
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- Metric.ediamstatement and proof · cited by 159
- Metric.IsCoverstatement · cited by 51
- Metric.edist_le_ediam_of_memproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- Metric.coveringNumber_eq_one_of_ediam_leproof · cited by 3