\begin{definition}[Definition:Closed Set/Real Analysis/Real Euclidean Space]
Let $n\geq1$ be a natural number.
Let $S \subseteq \R^n$ be a subset.
Then $S$ is '''closed (in $\R^n$)''' {{iff}} its complement $\R^n \setminus S$ is an open set.
\end{definition}