Theorems · Theorem · general topology
Metric.cobounded_eq_cocompact
∀ {α : Type u} [inst : PseudoMetricSpace α] [ProperSpace α], Bornology.cobounded α = Filter.cocompact α- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 118 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Filterstatement · cited by 8,121
- Bot.botproof · cited by 4,720
- Nontrivialproof · cited by 2,416
- PseudoMetricSpacestatement and proof · cited by 1,550
- LE.le.antisymmproof · cited by 507
- ProperSpacestatement and proof · cited by 190
- Bornology.coboundedstatement · cited by 162
- Filter.cocompactstatement · cited by 141
- ProperSpace.isCompact_closedBallproof · cited by 40
- Filter.HasBasis.ge_iffproof · cited by 28
- IsCompact.compl_mem_cocompactproof · cited by 13
Cited by8
Results whose statement or proof uses this declaration.
- spectrum.nonemptyproof · cited by 8
- tendsto_norm_cocompact_atTopproof · cited by 6
- Complex.exists_rootproof · cited by 1
- tendsto_dist_left_cocompact_atTopproof · cited by 1
- comap_dist_left_atTop_eq_cocompactproof · cited by 1
- tendsto_norm_cocompact_atTop'proof · cited by 1
- Polynomial.isProperMap_evalproof · cited by 1
- tendsto_dist_right_cocompact_atTopproof · cited by 0