Theorems · Definition · general topology
Metric.coveringNumber
{X : Type u_1} → [PseudoEMetricSpace X] → NNReal → Set X → ℕ∞The covering number (or internal covering number) of a set A for radius ε is
the minimal cardinality (in ℕ∞) of an ε-cover contained in A.
- Cited by
- 19 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.
Cites7
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
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.encardproof · cited by 327
- Metric.IsCoverproof · cited by 51
Cited by20
Results whose statement or proof uses this declaration.
- Metric.minimalCoverproof · cited by 4
- Metric.externalCoveringNumber_le_coveringNumberstatement · cited by 3
- Metric.coveringNumber_eq_one_of_ediam_lestatement and proof · cited by 3
- Metric.IsCover.coveringNumber_le_encardstatement · cited by 3
- Metric.coveringNumber_le_packingNumberstatement and proof · cited by 2
- Metric.coveringNumber_emptystatement · cited by 1
- Metric.coveringNumber_eq_zerostatement · cited by 1
- Metric.coveringNumber_le_encard_selfstatement · cited by 1
- Isometry.coveringNumber_image'statement · cited by 1
- Metric.exists_set_encard_eq_coveringNumberstatement and proof · cited by 0
- Metric.isCover_minimalCoverstatement and proof · cited by 0
- Metric.coveringNumber_antistatement · cited by 0