Theorems · Theorem · general topology
Metric.iUnion_closedBall_nat
∀ {α : Type u} [inst : PseudoMetricSpace α] (x : α), ⋃ n, Metric.closedBall x ↑n = Set.univ- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 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 · cited by 53,352
- Realstatement · cited by 25,697
- Set.univstatement · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- Metric.closedBallstatement · cited by 704
- exists_nat_geproof · cited by 20
- Set.iUnion_eq_univ_iffproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Metric.iUnion_inter_closedBall_natproof · cited by 2
- MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zeroproof · cited by 1