Theorems · Theorem · general topology
Metric.ediam_subsingleton
∀ {X : Type u_2} {s : Set X} [inst : PseudoEMetricSpace X], s.Subsingleton → Metric.ediam s = 0The diameter of a subsingleton vanishes.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 150 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.Subsingletonstatement and proof · cited by 276
- Metric.ediamstatement · cited by 159
- nonpos_iff_eq_zeroproof · cited by 100
- PseudoEMetricSpace.edist_selfproof · cited by 50
- Metric.ediam_leproof · cited by 13
Cited by6
Results whose statement or proof uses this declaration.
- Metric.ediam_singletonproof · cited by 10
- Metric.ediam_emptyproof · cited by 7
- Metric.diam_subsingletonproof · cited by 2
- Metric.ediam_eq_zero_iffproof · cited by 1
- EMetric.diam_subsingletonproof · cited by 0
- Set.Subsingleton.ediam_eqproof · cited by 0