Theorems · Theorem · general topology
Metric.sphere_union_ball
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, Metric.sphere x ε ∪ Metric.ball x ε = Metric.closedBall x ε- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites8
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement and proof · cited by 704
- Metric.spherestatement and proof · cited by 371
- Set.union_commproof · cited by 99
- Metric.ball_union_sphereproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCellproof · cited by 4