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