Theorems · Theorem · general topology
IsUltrametricDist.frontier_closedBall_eq_empty
∀ {X : Type u_1} [inst : PseudoMetricSpace X] [IsUltrametricDist X] (x : X) {r : ℝ},
r ≠ 0 → frontier (Metric.closedBall x r) = ∅- Defined in
- Mathlib.Topology.MetricSpace.Ultra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- frontierstatement · cited by 214
- IsUltrametricDiststatement and proof · cited by 177
- isClopen_iff_frontier_eq_emptyproof · cited by 6
- IsUltrametricDist.isClopen_closedBallproof · cited by 2
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