Theorems · Theorem · general topology
Metric.externalCoveringNumber_eq_one_of_ediam_le
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {A : Set X} {ε : NNReal},
A.Nonempty → Metric.ediam A ≤ ↑ε → Metric.externalCoveringNumber ε A = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 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.
Cites13
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
- ENatstatement · cited by 4,985
- NNRealstatement and proof · cited by 4,310
- Set.Nonemptystatement and proof · cited by 2,627
- le_antisymmproof · cited by 2,068
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- LE.le.trans_eqproof · cited by 328
- Metric.ediamstatement and proof · cited by 159
- Metric.externalCoveringNumberstatement · cited by 14
- Metric.coveringNumber_eq_one_of_ediam_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Metric.externalCoveringNumber_singletonproof · cited by 0
- Metric.externalCoveringNumber_le_one_of_ediam_leproof · cited by 0