Theorems · Theorem · general topology
Metric.isCover_iff_subset_iUnion_closedBall
∀ {X : Type u_1} [inst : PseudoMetricSpace X] {ε : NNReal} {s N : Set X},
Metric.IsCover ε s N ↔ s ⊆ ⋃ y ∈ N, Metric.closedBall y ↑ε- Defined in
- Mathlib.Topology.MetricSpace.Cover
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.ofPredproof · cited by 6,101
- NNRealstatement and proof · cited by 4,310
- Set.iUnionstatement · cited by 2,483
- PseudoMetricSpacestatement and proof · cited by 1,550
- NNReal.toRealstatement · cited by 1,260
- Metric.closedBallstatement · cited by 704
- NNDist.nndistproof · cited by 235
- Metric.IsCoverstatement · cited by 51
Cited by3
Results whose statement or proof uses this declaration.
- Metric.isCover_iff_subset_cthickeningproof · cited by 3
- Metric.IsCover.of_subset_iUnion_closedBallproof · cited by 1
- Metric.IsCover.subset_iUnion_closedBallproof · cited by 0