Theorems · Theorem · general topology
Metric.closedBall_compl_subset_of_mem_cocompact
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α},
s ∈ Filter.cocompact α → ∀ (c : α), ∃ r, (Metric.closedBall c r)ᶜ ⊆ s- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 118 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.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Filterstatement · cited by 8,121
- Compl.complstatement · cited by 2,925
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Filter.cocompactstatement and proof · cited by 141
- Metric.cobounded_le_cocompactproof · cited by 4
- Bornology.IsCobounded.closedBall_compl_subsetproof · cited by 1
Cited by4
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
- ZeroAtInftyContinuousMapClass.norm_leproof · cited by 0