Theorems · Theorem · general topology
EMetric.ball_disjoint
Deprecated since 2026-01-24Use Metric.eball_disjoint instead.
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {ε₁ ε₂ : ENNReal},
ε₁ + ε₂ ≤ edist x y → Disjoint (Metric.eball x ε₁) (Metric.eball y ε₂)Alias of Metric.eball_disjoint.
- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites7
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
- Disjointstatement · cited by 2,201
- PseudoEMetricSpacestatement · cited by 1,536
- EDist.ediststatement · cited by 735
- Metric.eballstatement · cited by 294
- Metric.eball_disjointproof · cited by 1
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