  A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of
subsets of $X$ called balls (or entourages of the diagonal in $X\times X$)
defined in such a way that $\mathcal{B}$ can be considered as the asymptotic
counterpart of a uniform topological space. The aim of this paper is to study
two concrete balleans defined by the ideals in the Boolean algebra of all
subsets of $X$ and their hyperballeans, with particular emphasis on their
connectedness structure, more specifically the number of their connected
components.
