Theorems · Definition · general topology
Metric.minimalCover
{X : Type u_1} → [PseudoEMetricSpace X] → NNReal → Set X → Set XA finite internal ε-cover of a set A by closed balls with minimal cardinality.
It is defined as the empty set if no such finite cover exists.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 150 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.
Cites6
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
- Top.topproof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.coveringNumberproof · cited by 19
- Metric.exists_set_encard_eq_coveringNumberproof · cited by 0
Cited by4
Results whose statement or proof uses this declaration.
- Metric.minimalCover_subsetstatement · cited by 0
- Metric.isCover_minimalCoverstatement · cited by 0
- Metric.encard_minimalCoverstatement · cited by 0
- Metric.finite_minimalCoverstatement · cited by 0