Theorems · Theorem · general topology
Metric.ediam_singleton
∀ {X : Type u_2} {x : X} [inst : PseudoEMetricSpace X], Metric.ediam {x} = 0The extended diameter of a singleton vanishes
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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 and proof · cited by 1,536
- Metric.ediamstatement · cited by 159
- Set.subsingleton_singletonproof · cited by 36
- Metric.ediam_subsingletonproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.hausdorffMeasure_zero_singletonproof · cited by 5
- MeasureTheory.Measure.nullSingletonClass_hausdorffproof · cited by 5
- Metric.ediam_tripleproof · cited by 2
- Metric.ediam_pairproof · cited by 2
- Metric.ediam_zeroproof · cited by 1
- Metric.ediam_oneproof · cited by 1
- ediam_smul₀proof · cited by 1
- EMetric.diam_singletonproof · cited by 0
- Metric.externalCoveringNumber_singletonproof · cited by 0
- Metric.coveringNumber_singletonproof · cited by 0