Theorems · Theorem · general topology
Metric.IsCover.of_subset_cthickening_of_lt
∀ {X : Type u_1} [inst : PseudoMetricSpace X] {ε : NNReal} {s N : Set X} {δ : NNReal},
s ⊆ Metric.cthickening (↑ε) N → ε < δ → Metric.IsCover δ s N- Defined in
- Mathlib.Topology.MetricSpace.Cover
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites11
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
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- PseudoMetricSpacestatement and proof · cited by 1,550
- NNReal.toRealstatement and proof · cited by 1,260
- LE.le.trans_ltproof · cited by 795
- Metric.cthickeningstatement and proof · cited by 113
- Metric.IsCoverstatement · cited by 51
- NNReal.zero_le_coeproof · cited by 13
- Metric.cthickening_subset_iUnion_closedBall_of_ltproof · cited by 2
- Metric.IsCover.of_subset_iUnion_closedBallproof · cited by 1
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