Pol, R.; Chaber, J. Note on the Wijsman hyperspaces of completely metrizable spaces. (English) Zbl 1098.54006 Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 5, No. 3, 827-832 (2002). The authors consider the hyperspace \(CL(X)\) of nonempty closed subsets of a completely metrizable space \(X\) endowed with the Wijsman topology \(\tau_{W_d}\). When \(X\) is separable and \(d\) and \(e\) are two metrics generating the topology of \(X\) then every countable set closed in \((CL(X),\,\tau_{W_e})\) has isolated points in \((CL(X),\,\tau_{W_d})\). In the case \(d=e\) this statement implies a theorem of Costantini on topological completeness of \((CL(X),\,\tau_{W_d})\). In this paper it is shown that for a nonseparable space \(X\) the hyperspace \((CL(X),\,\tau_{W_d})\) may contain a closed copy of the rationals. This answers a question of Zsilinszky. Reviewer: Zvonko Čerin (Zagreb) Cited in 8 Documents MSC: 54B20 Hyperspaces in general topology PDFBibTeX XMLCite \textit{R. Pol} and \textit{J. Chaber}, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 5, No. 3, 827--832 (2002; Zbl 1098.54006) Full Text: EuDML