Hyperspaces of Banach Spaces with the Attouch—Wets Topology

Let X be an infinite-dimensional Banach space with weight τ. By Cld AW (X), we denote the hyperspace of nonempty closed sets in X with the Attouch—Wets topology. By Fin AW (X), Comp AW (X) and Bdd AW (X), we denote the subspaces of Cld AW (X) consisting of finite sets, compact sets and bounded closed sets, respectively. In this paper, it is proved that