Theorems · Theorem · general topology
IsUltrametricDist.isClosed_ball
∀ {X : Type u_1} [inst : PseudoMetricSpace X] [IsUltrametricDist X] (x : X) (r : ℝ), IsClosed (Metric.ball x r)- Defined in
- Mathlib.Topology.MetricSpace.Ultra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Compl.complproof · cited by 2,925
- Disjointproof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement and proof · cited by 735
- LT.lt.not_geproof · cited by 305
- le_or_gtproof · cited by 269
- IsUltrametricDiststatement and proof · cited by 177
- dist_selfproof · cited by 116
- isOpen_compl_iffproof · cited by 63
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.isClopen_ballproof · cited by 1