Cofinite subset

of a set $X$

A subset $A$ of $X$ for which the relative complement $X \setminus A$ is finite.

The family $\mathcal{F}(X)$ of cofinite subsets of $X$ forms a filter, known as the Fréchet filter on $X$. It is contained in any non-principal ultrafilter on $X$.

The cofinite subsets of $X$, together with the empty set, constitute the open sets of a topology on $X$, known as the cofinite topology.