Let $d$ be a metric on a set $X$, and let $ B=\{B(p,e) = \{y\in X \mid d(p, y)<\epsilon \}\text{for every $p\in X$ and every $\epsilon>0$}\} $ For $B$ to be the basis of a topology on $X$, then $\emptyset\in B$, but I don't see how this can be guaranteed since $\epsilon>0$.
Thanks so much!