Theorems · Theorem · general topology
Bornology.IsCobounded.closedBall_compl_subset
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α},
Bornology.IsCobounded s → ∀ (c : α), ∃ r, (Metric.closedBall c r)ᶜ ⊆ s- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 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.
Cites7
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
- Compl.complstatement · cited by 2,925
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Bornology.IsCoboundedstatement and proof · cited by 23
- Metric.isCobounded_iff_closedBall_compl_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Metric.closedBall_compl_subset_of_mem_cocompactproof · cited by 4