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Theorems · Definition · general topology

Filter.IsBasis.filterBasis

{α : Type u_1} → {ι : Sort u_4} → {p : ι → Prop} → {s : ι → Set α} → Filter.IsBasis p s → FilterBasis α

Constructs a filter basis from an indexed family of sets satisfying IsBasis.

Defined in
Mathlib.Order.Filter.Bases.Basic
Cited by
4 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.IsBasis.filter · cited by 6IsBasis.filterFilter.IsBasis.mem_filter_iff · cited by 1IsBasis.mem_filter_iffUniformFun.basis · cited by 1UniformFun.basisFilter.IsBasis.filter_eq_generate · cited by 1IsBasis.filter_eq_generateFilter.IsBasis.mem_filterBasis_iff · cited by 0IsBasis.mem_filterBasis_i…Filter.IsBasis.filterBasis.congr_simp · cited by 0filterBasis.congr_simpSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredFilterBasis · cited by 23FilterBasisFilter.IsBasis · cited by 14Filter.IsBasisIsBasis.filterBasisCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.