Theorems · Theorem · general topology
Metric.mem_cocompact_of_closedBall_compl_subset
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α] [ProperSpace α] (c : α),
(∃ r, (Metric.closedBall c r)ᶜ ⊆ s) → s ∈ Filter.cocompact α- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- Compl.complstatement and proof · cited by 2,925
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement and proof · cited by 704
- ProperSpacestatement and proof · cited by 190
- Filter.cocompactstatement · cited by 141
- ProperSpace.isCompact_closedBallproof · cited by 40
- Filter.mem_cocompactproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Metric.mem_cocompact_iff_closedBall_compl_subsetproof · cited by 1
- Filter.tendsto_cocompact_cocompact_of_normproof · cited by 1
- CocompactMapClass.norm_leproof · cited by 0