  For any compact Hausdorff space $K$ we construct a canonical finitary coarse
structure $\mathcal E_{X,K}$ on the set $X$ of isolated points of $K$. This
construction has two properties:
  $\bullet$ If a finitary coarse space $(X,\mathcal E)$ is metrizable, then its
coarse structure $\mathcal E$ coincides with the coarse structure $\mathcal
E_{X,\bar X}$ generated by the Higson compactification $\bar X$ of $X$;
  $\bullet$ A compact Hausdorff space $K$ coincides with the Higson
compactification of the coarse space $(X,\mathcal E_{X,K})$ if the set $X$ is
dense in $K$ and the space $K$ is Frechet-Urysohn.
  This implies that a compact Hausdorff space $K$ is homeomorphic to the Higson
corona of some finitary coarse space if one of the following conditions holds:
(i) $K$ is perfectly normal; (ii) $K$ has weight $w(K)\le\omega_1$ and
character $\chi(K)<\mathfrak p$. Under CH every (zero-dimensional) compact
Hausdorff space of weight $\le\omega_1$ is homeomorphic to the Higson (resp.
binary) corona of some cellular finitary coarse space.
