Theorems · Theorem · general topology
Metric.packingNumber_two_mul_le_externalCoveringNumber
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] (ε : NNReal) (A : Set X),
Metric.packingNumber (2 * ε) A ≤ Metric.externalCoveringNumber ε AThe packing number of a set A for radius 2 * ε is at most the external covering number
of A for radius ε.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 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.
Cites21
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
- ENNRealproof · cited by 9,879
- Set.Elemproof · cited by 7,166
- ENatstatement · cited by 4,985
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- Cardinal.mkproof · cited by 942
- EDist.edistproof · cited by 735
- add_le_addproof · cited by 666
- two_mulproof · cited by 232
- Cardinal.toENatproof · cited by 92
Cited by2
Results whose statement or proof uses this declaration.
- Metric.coveringNumber_subset_leproof · cited by 0
- Metric.coveringNumber_two_mul_le_externalCoveringNumberproof · cited by 0