Theorems · Theorem · general topology
Metric.exists_set_encard_eq_packingNumber
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {A : Set X} {ε : NNReal},
Metric.packingNumber ε A ≠ ⊤ → ∃ C ⊆ A, C.Finite ∧ Metric.IsSeparated (↑ε) C ∧ C.encard = Metric.packingNumber ε A- Cited by
- 0 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.
Cites22
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.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- NNRealstatement and proof · cited by 4,310
- Set.Nonemptyproof · cited by 2,627
- iSupproof · cited by 2,415
- Set.Finitestatement and proof · cited by 1,814
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- Set.encardstatement and proof · cited by 327
- Set.eq_empty_or_nonemptyproof · cited by 248
- iSup_congr_Propproof · cited by 247
Cited by1
Results whose statement or proof uses this declaration.
- Metric.maximalSeparatedSetproof · cited by 5