Hyperspaces of Banach spaces with the Attouch-Wets topology (Q1876103)

In what follows all hyperspaces (of a Banach space \(X\)) are endowed with the Attouch-Wets topology. The main result asserts that both the hyperspace of all finite subsets and that of all compact subsets are homeomorphic to the product \(\ell_2(\tau)\times \ell_2^f\), and the hyperspace of all bounded closed subsets is homeomorphic to \(\ell_2(2^\tau)\times \ell_2^f\). To show this, the authors use a topological characterization of \(\ell_2(\tau)\times \ell_2^f\) (a \(\sigma\)-completely metrizable AR with weight \(\tau\) having certain universal property) proved in their earlier paper [Tsukuba J. Math. 27, 143--159 (2003; Zbl 1035.57011)].