Theorems · Theorem · general topology
Metric.ediam_univ_eq_top_iff_noncompact
∀ {α : Type u} [inst : PseudoMetricSpace α] [ProperSpace α], Metric.ediam Set.univ = ⊤ ↔ NoncompactSpace α- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceProperSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 9,680
- Set.univstatement and proof · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- ProperSpacestatement and proof · cited by 190
- Metric.ediamstatement and proof · cited by 159
- NoncompactSpacestatement · cited by 21
- Metric.isBounded_iff_ediam_ne_topproof · cited by 5
- not_compactSpace_iffproof · cited by 1
- Metric.compactSpace_iff_isBounded_univproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Metric.ediam_univ_of_noncompactproof · cited by 1