Theorems · Definition · general topology
Metric.externalCoveringNumber
{X : Type u_1} → [PseudoEMetricSpace X] → NNReal → Set X → ℕ∞The external covering number of a set A in X for radius ε is the minimal cardinality
(in ℕ∞) of an ε-cover by points in X (not necessarily 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.
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 by14
Results whose statement or proof uses this declaration.
- Metric.externalCoveringNumber_le_coveringNumberstatement · cited by 3
- Metric.externalCoveringNumber_eq_one_of_ediam_lestatement · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberstatement · cited by 2
- Metric.externalCoveringNumber_emptystatement · cited by 1
- Metric.externalCoveringNumber_eq_zerostatement · cited by 1
- Metric.externalCoveringNumber_le_encard_selfstatement · cited by 1
- Metric.externalCoveringNumber_mono_setstatement · cited by 1
- Metric.externalCoveringNumber_zerostatement · cited by 1
- Metric.IsCover.externalCoveringNumber_le_encardstatement · cited by 1
- Metric.externalCoveringNumber_antistatement · cited by 0
- Metric.externalCoveringNumber_le_one_of_ediam_lestatement · cited by 0
- Metric.externalCoveringNumber_pos_iffstatement · cited by 0