Theorems · Theorem · general topology
Metric.ediam_eq_zero_iff
∀ {X : Type u_2} {s : Set X} [inst : EMetricSpace X], Metric.ediam s = 0 ↔ s.Subsingleton- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.Subsingletonstatement · cited by 276
- EMetricSpacestatement and proof · cited by 242
- Metric.ediamstatement and proof · cited by 159
- Metric.edist_le_ediam_of_memproof · cited by 20
- Metric.ediam_subsingletonproof · cited by 6
- edist_le_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- EMetric.diam_eq_zero_iffproof · cited by 0