So I'm covering material for my upcoming final exam, and I have a sneaking suspicion that my teacher will ask us to prove the following theorem:
A subset $G$ of $\mathbb{R}^n$ is open iff the complement of $G$ is closed.
He's hinted at it a couple times, and honestly, I don't know where to start. Thanks for the help.
Definitions (copied from comments): A set is open if every point of the set is an interior point, meaning that the set contains some ball of positive radius at any one of the interior points. A closed set is one that contains all of its accumulation points.