  A set $X$ endowed with a coarse structure is called ballean or coarse space.
For a ballean $(X, \mathcal{E})$, we say that two subsets $A$, $B$ of $X$ are
close (linked) if there exists an entourage $E\in \mathcal{E}$ such that
$A\subseteq E [B]$, $B\subseteq E[A]$ (either $A, B$ are bounded or contain
unbounded close subsets). We explore the following general question: which
information about a ballean is contained and can be extracted from the
relations of closeness and linkness.
