Theorems · Theorem · general topology
Metric.ediam_empty
∀ {X : Type u_2} [inst : PseudoEMetricSpace X], Metric.ediam ∅ = 0The diameter of the empty set vanishes
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 7 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_emptyproof · cited by 16
- Metric.ediam_subsingletonproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Real.ediam_Iccproof · cited by 5
- Real.ediam_eqproof · cited by 4
- Real.ediam_Iooproof · cited by 3
- Metric.ediam_iUnion_mem_optionproof · cited by 2
- MeasureTheory.Measure.mkMetric_le_liminf_tsumproof · cited by 2
- ediam_smul₀proof · cited by 1
- EMetric.diam_emptyproof · cited by 0