Theorems · Theorem · general topology
Metric.coveringNumber_two_mul_le_externalCoveringNumber
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] (ε : NNReal) (A : Set X),
Metric.coveringNumber (2 * ε) A ≤ Metric.externalCoveringNumber ε A- Cited by
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- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites13
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
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.eq_empty_or_nonemptyproof · cited by 248
- Metric.coveringNumberstatement · cited by 19
- Metric.externalCoveringNumberstatement · cited by 14
- Metric.coveringNumber_le_packingNumberproof · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberproof · cited by 2
- Metric.externalCoveringNumber_emptyproof · cited by 1
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