Theorems · Theorem · general topology
Metric.diam_univ_of_noncompact
∀ {α : Type u} [inst : PseudoMetricSpace α] [ProperSpace α] [NoncompactSpace α], Metric.diam Set.univ = 0- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.univstatement · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.toRealproof · cited by 859
- ProperSpacestatement and proof · cited by 190
- Metric.diamstatement · cited by 74
- NoncompactSpacestatement and proof · cited by 21
- Metric.ediam_univ_of_noncompactproof · cited by 1
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