Let X is a non empty set, and then the collection of subsets of X whose compliments are finite along with (empty set), forms a topology on X, and is called co-finite topology.

Example:
            Let  with topology  is a co-finite topology because the compliments of all the subsets of X are finite.

Note:
            It may be noted that every infinite set may or may not be co-finite topology, for this suppose  (set of real numbers which is infinite set) with topology  is a co-finite topology because compliments of all the members of topology along with empty set are finite.

Remark:
            If X is finite, then topology is discrete. For a subset of X belongs to if and only if, it is either empty or its compliment is finite. When X is finite, the compliment of each of its subset is finite and therefore, each subset of X belongs to. Hence is the discrete topology on X.