Theorems · Definition · general topology
FilterBasis.filter
{α : Type u_1} → FilterBasis α → Filter αThe filter associated to a filter basis.
- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- FilterBasisstatement and proof · cited by 23
Cited by24
Results whose statement or proof uses this declaration.
- FilterBasis.hasBasisstatement · cited by 10
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfproof · cited by 8
- Filter.IsBasis.filterproof · cited by 6
- FilterBasis.generatestatement and proof · cited by 4
- AddGroupFilterBasis.nhds_zero_eqstatement and proof · cited by 4
- FilterBasis.mem_filter_of_memstatement · cited by 4
- GroupFilterBasis.nhds_one_eqstatement and proof · cited by 4
- SeminormFamily.withSeminorms_of_nhdsstatement and proof · cited by 3
- AddGroupFilterBasis.Nproof · cited by 3
- GroupFilterBasis.Nproof · cited by 3
- FilterBasis.mem_filter_iffstatement · cited by 3
- krullTopology_mem_nhds_one_iffproof · cited by 2