Theorems · Definition · general topology
Metric.closedBall
{α : Type u} → [PseudoMetricSpace α] → α → ℝ → Set αclosedBall x ε is the set of all points y with dist y x ≤ ε
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 704 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 1,950 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
Cited by764
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.closedCellproof · cited by 70
- Metric.ball_subset_closedBallstatement · cited by 46
- Metric.mem_closedBallstatement · cited by 42
- ProperSpace.isCompact_closedBallstatement · cited by 40
- Metric.nhds_basis_closedBallstatement · cited by 38
- Metric.isClosed_closedBallstatement · cited by 28
- Metric.sphere_subset_closedBallstatement · cited by 24
- Metric.closedBall_mem_nhdsstatement · cited by 20
- Metric.closedBall_subset_ballstatement · cited by 20
- closure_ballstatement and proof · cited by 20
- Metric.isBounded_closedBallstatement and proof · cited by 19
- Metric.closedBall_subset_closedBallstatement · cited by 18
Showing the 200 most cited of 764.