Theorems · Theorem · general topology
IsUltrametricDist.closedBall_eq_of_mem
∀ {X : Type u_1} [inst : PseudoMetricSpace X] [IsUltrametricDist X] {x y : X} {r : ℝ},
y ∈ Metric.closedBall x r → Metric.closedBall x r = Metric.closedBall y r- Defined in
- Mathlib.Topology.MetricSpace.Ultra.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LE.le.transproof · cited by 3,151
- Set.extproof · cited by 2,266
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- Metric.closedBallstatement and proof · cited by 704
- dist_commproof · cited by 188
- IsUltrametricDiststatement and proof · cited by 177
- max_leproof · cited by 71
- IsUltrametricDist.dist_triangle_maxproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- IsUltrametricDist.isOpen_closedBallproof · cited by 3
- IsUltrametricDist.closedBall_eq_or_disjointproof · cited by 1
- IsUltrametricDist.closedBall_subset_trichotomyproof · cited by 0