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Hyperspaces of Normed Linear Spaces with the Attouch–Wets Topology |
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| Authors: | Taras Banakh Masayuki Kurihara and Katsuro Sakai |
| Institution: | (1) Department of Mathematics, Lviv National University, Lviv, 79000, Ukraine;(2) Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan |
| Abstract: | Let Cld AW (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 Cld AW (X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then Cld AW (X) is homeomorphic to a Hilbert space with weight 2 w(X). |
| Keywords: | hyperspace Attouch– Wets topology normed linear space Banach space Hilbert space AR |
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