Sums and Products of Continuous Real-Valued Functions

Let $E\subseteq \mathbb{R}^n$, let $u,v:E\to\mathbb{R}$, and let $a\in E$. Suppose that $u$ and $v$ are continuous at $a$. Then the functions $u+v:E\to\mathbb{R}$ and $uv:E\to\mathbb{R}$ are continuous at $a$.