Let ''<math>X''</math> be a set with <math>A=\{A_i\}_{i\in I}</math> a family of subsets of ''<math>X''</math>. Then the collection ''<math>A''</math> has the finite intersection property (FIP), if any finite subcollection ''<math>J''\subseteq ⊆ ''I''</math> has non-empty intersection <math>\bigcap_{i\in J} A_i.</math>
