$X \in \mathbb{R}^{n}$ is a limited subset. Prove that $\mathbb{R}^{n} - X$ has exactly one ilimited connected component, for $n > 1$.
I tried to show that if $\mathbb{R}^{n} - X$ has more than one ilimited connected component, then $X \in \mathbb{R}^{n}$ isn't limited, but i don't even know how to start. Any help would be greatly appreciated.