In a metric space $\displaystyle (S,d)$, let $\displaystyle A$ and $\displaystyle B$ be disjoint closed subsets of$\displaystyle S$. Prove that $\displaystyle \exists$ disjoint open sets $\displaystyle U$ and $\displaystyle V$ of $\displaystyle S$ such that $\displaystyle A \subset U$ and $\displaystyle B \subset V$.