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Note on the Wijsman hyperspaces of completely metrizable spaces

J. ChaberR. Pol — 2002

Bollettino dell'Unione Matematica Italiana

We consider the hyperspace C L X of nonempty closed subsets of completely metrizable space X endowed with the Wijsman topologies τ W d . If X is separable and d , e are two metrics generating the topology of X , every countable set closed in C L X , τ W e has isolated points in C L X , τ W d . For d = e , this implies a theorem of Costantini on topological completeness of C L X , τ W d . We show that for nonseparable X the hyperspace C L X , τ W d may contain a closed copy of the rationals. This answers a question of Zsilinszky.

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