  This paper is devoted to dualization of paracompactness to the coarse
category via the concept of $R$-disjointness. Property A of G.Yu can be seen as
a coarse variant of amenability via partitions of unity and leads to a
dualization of paracompactness via partitions of unity. On the other hand,
finite decomposition complexity of G.Yu and straight finite decomposition
complexity of Dranishnikov-Zarichnyi employ $R$-disjointness as the main
concept. We generalize both concepts to that of countable asymptotic dimension
and our main result shows that it is a subclass of of spaces with Property A.
In addition, it gives a necessary and sufficient condition for spaces of
countable asymptotic dimension to be of finite asymptotic dimension.
