(1) Department of Mathematics, Lviv National University, Lviv, 79000, Ukraine;(2) Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan
Abstract:
Let CldAW(X) be the hyperspace of nonempty closed subsets of a normed linear space X with the Attouch–Wets topology. It is shown that the space CldAW(X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then CldAW(X) is homeomorphic to a Hilbert space with weight 2w(X).