Theorems · Theorem · general topology
EMetric.diam_empty
Deprecated since 2026-01-04Use Metric.ediam_empty instead.
∀ {X : Type u_2} [inst : PseudoEMetricSpace X], Metric.ediam ∅ = 0Alias of Metric.ediam_empty.
The diameter of the empty set vanishes
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 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.
Cites5
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
- Metric.ediamstatement · cited by 159
- Metric.ediam_emptyproof · cited by 7
Cited by0
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