Define the limit set $\Lambda(G)$ of a Kleinian group $G$. Assuming that $G$ has no finite orbit in $\mathbb{H}^{3} \cup S_{\infty}^{2}$, and that $\Lambda(G) \neq \emptyset$, prove that if $E \subset \mathbb{C} \cup\{\infty\}$ is any non-empty closed set which is invariant under $G$, then $\Lambda(G) \subset E$.