Topology, complements of finite sets

Let R be the set of real numbers, then let $\displaystyle \omega$ be the set of all complements of finite sets and the empty set. Prove that (R, $\displaystyle \omega$) is a topological structure.

I was able to prove that it's closed under finite intersections, and I was able to show that the full set is in $\displaystyle \omega$, but I'm having difficulty proving that it's closed under arbitrary unions... Any help would be appreciated. This is not for homework of anykind.