Hi,

I don't know how to prove this exercise, actually I don't even know how to start :

Let $\displaystyle (E,d)$ is separable metric space. Prove that its borel $\displaystyle \sigma$-algebra $\displaystyle B(E)$ is generated by system $\displaystyle U(x,\epsilon) = \left\{y \in E: d(y,x)<\epsilon\right\}$.

I would appreciate any hint.