Theorems · Theorem · general topology
Metric.IsCover.coveringNumber_le_encard
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {A C : Set X} {ε : NNReal},
C ⊆ A → Metric.IsCover ε A C → Metric.coveringNumber ε A ≤ C.encard- Cited by
- 3 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.
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
- ENatstatement · cited by 4,985
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.encardstatement and proof · cited by 327
- iInf_leproof · cited by 104
- Metric.IsCoverstatement and proof · cited by 51
- iInf₂_leproof · cited by 45
- Metric.coveringNumberstatement · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Metric.coveringNumber_eq_one_of_ediam_leproof · cited by 3
- Metric.coveringNumber_le_packingNumberproof · cited by 2
- Metric.coveringNumber_le_encard_selfproof · cited by 1