Let X {\displaystyle X} be set with A = { A i } i ∈ I {\displaystyle A=\{A_{i}\}_{i\in I}} a family of subsets of X {\displaystyle X} . Then the collection A {\displaystyle A} has the finite intersection property, if any finite subcollection J ⊂ I {\displaystyle J\subset I} has non-empty intersection ⋂ i ∈ J A i {\displaystyle \bigcap _{i\in J}A_{i}} .
