On a hyperspace of compact subsets which is homeomorphic to a non-separable Hilbert space

Let $X$ be a metrizable space and $\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}(X)$ be the hyperspace consisting of non-empty compact subsets of $X$ endowed with the Vietoris topology. In this paper, we give a necessary and sufficient condition on $X$ for $\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}(X)$ to be homeomorphic to a non-separable Hilbert space. Moreover, we consider the topological structure of pair $({\rm Comp}(\overline{X}),{\rm Fin}(X))$ofhyperspacesof$X$anditscompletion$\overline{X}$,where${\rm Fin}(X)$ is the hyperspace of non-empty finite sets in $X$.