Consider a nonempty set S with the discrete metric. What is the system of neighborhoods of a given $x \in S$ This is what I've thought :
 A set V  S is called neighborhood of x if there is some $\epsilon > 0$ such that $U(x,\epsilon ) \subseteq V $.
So I should first think about what the $\epsilon$ neighborhoods $U(x, \epsilon )$ of $x$ are, depending on the choice of $\epsilon > 0$?
I'm a bit stuck here, any help would be appreciated.

HINT: If $x\in S$, what is $U\left(\frac12\right)$? What subsets of $S$ have $U\left(\frac12\right)$ as a subset?
