Amsterdam properties of Wijsman hyperspaces

Cao, Jiling; Junnila, Heikki

doi:10.1090/S0002-9939-09-10072-2

Amsterdam properties of Wijsman hyperspaces
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by Jiling Cao and Heikki J. K. Junnila PDF

Proc. Amer. Math. Soc. 138 (2010), 769-776 Request permission

Abstract:

In this paper we show the following results: (i) there exists a separable metric space of the first category whose Wijsman hyperspace is almost countably subcompact; (ii) there exists a $\sigma$-discrete crowded metric space whose Wijsman hyperspace is countably base-compact. Neither of these can occur with Vietoris hyperspaces.

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