Theorems · Theorem · general topology
Metric.emetric_closedBall
Deprecated since 2026-01-24Use Metric.closedEBall_ofReal instead.
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ},
0 ≤ ε → Metric.closedEBall x (ENNReal.ofReal ε) = Metric.closedBall x εAlias of Metric.closedEBall_ofReal.
Closed balls defined using the distance or the edistance coincide
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
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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
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement · cited by 1,550
- ENNReal.ofRealstatement · cited by 863
- Metric.closedBallstatement · cited by 704
- Metric.closedEBallstatement · cited by 107
- Metric.closedEBall_ofRealproof · cited by 3
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