Theorems · Theorem · general topology
Filter.HasBasis.disjoint_cobounded_iff
∀ {α : Type u_2} [inst : Bornology α] {ι : Sort u_4} {p : ι → Prop} {s : ι → Set α} {l : Filter α},
l.HasBasis p s → (Disjoint l (Bornology.cobounded α) ↔ ∃ i, p i ∧ Bornology.IsBounded (s i))- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Bornology
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Filterstatement and proof · cited by 8,121
- Disjointstatement · cited by 2,201
- Filter.HasBasisstatement and proof · cited by 604
- Bornology.IsBoundedstatement · cited by 293
- Bornologystatement and proof · cited by 188
- Bornology.coboundedstatement · cited by 162
- Filter.HasBasis.disjoint_iff_leftproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Filter.disjoint_cobounded_iffproof · cited by 2