Theorems · Theorem · general topology
Metric.disjoint_closedBall_of_lt_infDist
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α} {r : ℝ},
r < Metric.infDist x s → Disjoint (Metric.closedBall x r) s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 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
- Realstatement and proof · cited by 25,697
- Disjointstatement · cited by 2,201
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Metric.infDiststatement and proof · cited by 68
- Disjoint.mono_leftproof · cited by 50
- Metric.closedBall_subset_ballproof · cited by 20
- Metric.disjoint_ball_infDistproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxproof · cited by 1