Theorems · Theorem · general topology
Metric.coveringNumber_subset_le
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {A B : Set X} {ε : NNReal},
A ⊆ B → Metric.coveringNumber ε A ≤ Metric.coveringNumber (ε / 2) B- Cited by
- 0 results in Mathlib
- 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
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- PseudoEMetricSpacestatement and proof · cited by 1,536
- pow_oneproof · cited by 894
- Metric.coveringNumberstatement · cited by 19
- Metric.packingNumberproof · cited by 14
- Metric.externalCoveringNumber_le_coveringNumberproof · cited by 3
- Metric.coveringNumber_le_packingNumberproof · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberproof · cited by 2
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