Theorems · Definition · general topology
Metric.packingNumber
{X : Type u_1} → [PseudoEMetricSpace X] → NNReal → Set X → ℕ∞The packing number of a set A for radius ε is the maximal cardinality (in ℕ∞)
of an ε-separated set in A.
- Cited by
- 14 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.
Cites8
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
- iSupproof · cited by 2,415
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- Set.encardproof · cited by 327
- Metric.IsSeparatedproof · cited by 28
Cited by15
Results whose statement or proof uses this declaration.
- Metric.maximalSeparatedSetproof · cited by 5
- Metric.encard_maximalSeparatedSetstatement and proof · cited by 3
- Metric.coveringNumber_le_packingNumberstatement and proof · cited by 2
- Metric.packingNumber_le_encard_selfstatement · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberstatement · cited by 2
- Metric.isCover_maximalSeparatedSetstatement and proof · cited by 1
- Metric.encard_le_of_isSeparatedstatement and proof · cited by 1
- Metric.exists_set_encard_eq_packingNumberstatement and proof · cited by 0
- Metric.IsSeparated.encard_le_packingNumberstatement · cited by 0
- Metric.coveringNumber_subset_leproof · cited by 0
- Metric.packingNumber_emptystatement · cited by 0
- Metric.packingNumber_eq_zerostatement · cited by 0