Finite subsets do not define a topology on an infinite set
= Finite subsets do not define a topology on an infinite set
On an infinite <set>, the family consisting of all finite subsets and the whole set need not be closed under arbitrary unions. On $\mathbb Z$, the union of the singleton subsets of $2\mathbb Z$ is infinite and proper, so this family is not a <topology>. It must not be confused with the <cofinite topology>, whose proper open sets have finite complements.