So, my professor asked me to prove a theorem, and I only have a question about PART of it.

Theorem: Let $\displaystyle X$ be a set and let $\displaystyle \mu$ be a metric on $\displaystyle X$. The set $\displaystyle B = \{\emptyset\} \cup \{B_r(x) : x \in X, r \in \mathbb{R}\}$ forms a basis for a topology on $\displaystyle X$.

My question is this: Is it necessary to union the empty set with the open balls? I don't understand why this is necessary.