Theorems · Theorem · general topology
EMetric.diam_subsingleton
Deprecated since 2026-01-04Use Metric.ediam_subsingleton instead.
∀ {X : Type u_2} {s : Set X} [inst : PseudoEMetricSpace X], s.Subsingleton → Metric.ediam s = 0Alias of Metric.ediam_subsingleton.
The diameter of a subsingleton vanishes.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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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
- PseudoEMetricSpacestatement · cited by 1,536
- Set.Subsingletonstatement · cited by 276
- Metric.ediamstatement · cited by 159
- Metric.ediam_subsingletonproof · cited by 6
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