Definition. 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 for any finite subcollection, J ⊂ I {\displaystyle J\subset I} , the intersection ⋂ i ∈ J A i {\displaystyle \bigcap _{i\in J}A_{i}} is non-empty.
