Theorems · Definition · general topology
Metric.ball
{α : Type u} → [PseudoMetricSpace α] → α → ℝ → Set αball x ε is the set of all points y with dist y x < ε
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 735 results in Mathlib
- Foundations
- Depth 90 from the axioms, rests on 1,947 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 by773
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.openCellproof · cited by 75
- Metric.ball_mem_nhdsstatement · cited by 64
- Metric.isOpen_ballstatement · cited by 63
- Metric.mem_ballstatement · cited by 47
- Metric.ball_subset_closedBallstatement and proof · cited by 46
- Metric.nhds_basis_ballstatement · cited by 41
- Metric.mem_ball_selfstatement · cited by 40
- convex_ballstatement · cited by 30
- Metric.mem_nhds_iffstatement · cited by 26
- Metric.isOpen_iffstatement and proof · cited by 22
- mem_ball_zero_iffstatement · cited by 22
- Metric.closedBall_subset_ballstatement · cited by 20
Showing the 200 most cited of 773.