  We define the direct sum of a countable family of pointed metric spaces in a
way resembling the direct sum of groups. Then we prove that if a family
consists of $0$-hyperbolic (in the sense of Gromov) and $D$-discrete spaces,
then its direct sum has asymptotic property C. The main example is a countable
direct sum of free groups of (possibly varying) finite rank. This is a
generalization of T. Yamauchi's result concernig the countable direct sum of
the integers.
