Dieudonné completeness of a space of closed subsets and extensions of an open-closed map

We prove: if X is a paracompact Hausdorff space, then the space 2X of all nonempty closed subsets of X with the Vietoris topology is Dieudonné complete. If f: X → Y is an open-closed continuous onto map and 2μ(X) is Dieudonné complete, then the extension μ(f): μ(X) → μ(Y) is open-closed, where μ(X) is the Dieudonné completion of X.