Theorems · Definition · general topology
Filter.IsBounded
{α : Type u_1} → (α → α → Prop) → Filter α → Propf.IsBounded r: the filter f is eventually bounded w.r.t. the relation r,
i.e. eventually, it is bounded by some uniform bound.
r will be usually instantiated with (· ≤ ·) or (· ≥ ·).
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallyproof · cited by 3,134
Cited by50
Results whose statement or proof uses this declaration.
- Filter.IsBoundedUnderproof · cited by 247
- Filter.isBounded_le_of_topstatement · cited by 75
- Filter.isBounded_ge_of_botstatement · cited by 55
- Filter.IsBounded.isCobounded_flipstatement and proof · cited by 8
- Filter.IsBounded.monostatement and proof · cited by 7
- Antitone.map_limsSup_of_continuousAtstatement and proof · cited by 6
- Monotone.map_limsInf_of_continuousAtstatement and proof · cited by 5
- Monotone.map_limsSup_of_continuousAtstatement and proof · cited by 5
- ClusterPt.limsSupstatement and proof · cited by 4
- Filter.IsBounded.isCobounded_lestatement and proof · cited by 4
- isBounded_ge_nhdsstatement · cited by 4
- isBounded_le_nhdsstatement · cited by 4