Theorems · Theorem · general topology
Metric.ediam_univ_of_noncompact
∀ {α : Type u} [inst : PseudoMetricSpace α] [ProperSpace α] [NoncompactSpace α], Metric.ediam Set.univ = ⊤- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.univstatement · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- ProperSpacestatement and proof · cited by 190
- Metric.ediamstatement · cited by 159
- NoncompactSpacestatement and proof · cited by 21
- Metric.ediam_univ_eq_top_iff_noncompactproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Metric.diam_univ_of_noncompactproof · cited by 0