Theorems · Theorem · general topology
EMetric.diam_eq_zero_iff
Deprecated since 2026-01-04Use Metric.ediam_eq_zero_iff instead.
∀ {X : Type u_2} {s : Set X} [inst : EMetricSpace X], Metric.ediam s = 0 ↔ s.SubsingletonAlias of Metric.ediam_eq_zero_iff.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
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Cites6
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
- Set.Subsingletonstatement · cited by 276
- EMetricSpacestatement · cited by 242
- Metric.ediamstatement · cited by 159
- Metric.ediam_eq_zero_iffproof · cited by 1
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