Theorems · Theorem · general topology
Filter.basis_sets
∀ {α : Type u_1} (l : Filter α), l.HasBasis (fun s => s ∈ l) id- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 21 definitions · 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 and proof · cited by 8,121
- Filter.HasBasisstatement · cited by 604
- Filter.exists_mem_subset_iffproof · cited by 7
Cited by105
Results whose statement or proof uses this declaration.
- mem_nhdsWithin_iff_exists_mem_nhds_interproof · cited by 12
- Filter.HasBasis.disjoint_iff_leftproof · cited by 11
- Filter.exists_antitone_basisproof · cited by 10
- Filter.mem_lift_setsproof · cited by 8
- regularSpace_TFAEproof · cited by 6
- UniformFun.postcomp_isUniformInducingproof · cited by 6
- UniformFun.hasBasis_nhdsproof · cited by 5
- Filter.limsup_eq_iInf_iSupproof · cited by 5
- Filter.mem_prod_self_iffproof · cited by 4
- balancedCore_mem_nhds_zeroproof · cited by 4
- UniformOnFun.uniformity_eqproof · cited by 4
- lebesgue_number_lemmaproof · cited by 4