Theorems · Theorem · general topology
Metric.cobounded_le_cocompact
∀ {α : Type u} [inst : PseudoMetricSpace α], Bornology.cobounded α ≤ Filter.cocompact α- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- PseudoMetricSpacestatement and proof · cited by 1,550
- IsCompactproof · cited by 1,282
- Bornology.coboundedstatement · cited by 162
- Filter.cocompactstatement · cited by 141
- IsCompact.isBoundedproof · cited by 29
- Filter.HasBasis.ge_iffproof · cited by 28
- Filter.hasBasis_cocompactproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Metric.cobounded_eq_cocompactproof · cited by 8
- Metric.closedBall_compl_subset_of_mem_cocompactproof · cited by 4
- MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSetproof · cited by 2
- tendsto_cocompact_of_tendsto_dist_comp_atTopproof · cited by 0