I began reading Rudin's Real and Complex Analysis, and I have a question about the following:
Rudin defines a topology $T$ in a set $X$ as the collection of subsets of $X$ such that
(i) empty set and $X$ are members of $T$ (ii) members of $T$ are closed under arbitrary unions (iii) members of $T$ are closed under finite intersections.
He then says that if $X$ is a metric space and $T$ is the collection of all subsets of $X$ which are the arbitrary unions of open balls, then $T$ is a topology in $X$.
What I do not understand is how is empty set the arbitrary union of open balls?
Can anyone explain this to me?