Theorems · Theorem · general topology
Metric.closedEBall_top
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x : α), Metric.closedEBall x ⊤ = Set.univ- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.univstatement · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- le_topproof · cited by 411
- Metric.closedEBallstatement · cited by 107
- Set.mem_ofPredproof · cited by 104
- Set.eq_univ_of_forallproof · cited by 80
Cited by3
Results whose statement or proof uses this declaration.
- convex_closedEBallproof · cited by 1
- Real.volume_closedEBallproof · cited by 1
- EMetric.closedBall_topproof · cited by 0