User:Zero sharp/Finite intersection property

Definition
Let $$X$$ be set with $$A=\{A_i\}_{i\in I}$$ a family of subsets of $$X$$. Then the collection $$A$$ has the finite intersection property, if any finite subcollection $$J\subset I$$ has non-empty intersection $$\bigcap_{i\in J} A_i$$.