Densely continuous forms in Vietoris hyperspaces

For countably paracompact normal spaces X and locally compact separable metric spaces Y, a characterization is given for the closure of the set of densely continuous forms from X to Y in the hyperspace of nonempty closed subsets of X x Y under the Vietoris topology. This shows that for such X having no isolated points, every closed subset of X x R that is dense over X can be 'Vietoris approximated' by a semicontinuous function on X.