  We explore the connections between selection games on Hausdorff spaces and
their corresponding Vietoris space of compact subsets. These considerations
offer a similar relationship as the well-known relationship between
$\omega$-covers of $X$ and regular open covers of the finite powers of $X$. The
primary utility of this method is to establish similar relationships with
$k$-covers and the Vietoris space of compact subsets. Particularly, we show
that some commonly studied selection principles are equivalent to a related
hyperspace being Menger or Rothberger. We then apply these equivalences to
correct a flawed argument in a previous paper which attempted to show that a
Pawlikowski theorem is true for $k$-covers.
