  For a Hausdorff space $X$ we denote be $2^X$ the family of all closed subsets
of $X$. In this paper we continue to research relationships between closure
-type properties of hyperspaces over a space $X$ and covering properties of
$X$. We investigate selectors for sequence of subsets of the space $2^{X}$ with
the $Z^{+}$-topology and the upper Fell topology.
