Theorems · Definition · general topology
Filter.generate
{α : Type u} → Set (Set α) → Filter αgenerate g is the largest filter containing the sets g.
- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.GenerateSetsproof · cited by 3
Cited by34
Results whose statement or proof uses this declaration.
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- Filter.le_generate_iffstatement and proof · cited by 7
- Filter.giGeneratestatement and proof · cited by 6
- Filter.generate_eq_biInfstatement · cited by 5
- Filter.mem_generate_of_memstatement · cited by 5
- FilterBasis.generatestatement · cited by 4
- Filter.hasBasis_generatestatement · cited by 2
- Filter.iInf_eq_generatestatement · cited by 1
- Filter.HasBasis.eq_generatestatement · cited by 1
- Filter.IsCountablyGenerated.casesOnstatement and proof · cited by 1
- Filter.atBot_eq_generate_Iicstatement · cited by 1
- Filter.atBot_eq_generate_of_forall_exists_lestatement and proof · cited by 1