Theorems · Theorem · general topology
EMetric.mem_ball_self
Deprecated since 2026-01-24Use Metric.mem_eball_self instead.
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {ε : ENNReal}, 0 < ε → x ∈ Metric.eball x εAlias of Metric.mem_eball_self.
- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites5
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
- PseudoEMetricSpacestatement · cited by 1,536
- Metric.eballstatement · cited by 294
- Metric.mem_eball_selfproof · cited by 6
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