Theorems · Definition · general topology
Filter.IsBasis.filter
{α : Type u_1} → {ι : Sort u_4} → {p : ι → Prop} → {s : ι → Set α} → Filter.IsBasis p s → Filter αConstructs a filter from an indexed family of sets satisfying IsBasis.
- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- FilterBasis.filterproof · cited by 19
- Filter.IsBasisstatement and proof · cited by 14
- Filter.IsBasis.filterBasisproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Filter.IsBasis.hasBasisstatement · cited by 3
- Filter.HasBasis.filter_eqstatement · cited by 2
- CStarAlgebra.approximateUnitproof · cited by 2
- Filter.IsBasis.mem_filter_iffstatement · cited by 1
- Filter.generate_eq_generate_interproof · cited by 1
- Filter.IsBasis.filter_eq_generatestatement · cited by 1
- Filter.IsBasis.filter.congr_simpstatement and proof · cited by 0