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Arcwise connectedness of the complement in a hyperspace. (English) Zbl 0882.54005
Let \(X\) be a (metrizable) continuum and \(C(X)\) be its hyperspace of non-degenerate subcontinua. It is known that \(C(X)\) is arcwise connected. In this interesting paper the author shows that if \(\mathcal Y\) is a countable closed subset of \(C(X)\) and \(C(X)\smallsetminus \{Y\}\) is arcwise connected for every \(Y\in {\mathcal Y}\) then \(C(X)\smallsetminus {\mathcal Y}\) is arcwise connected. This answers a question of S. B. Nadler jun. [Hyperspaces of sets, Monogr. Textb. Pure Appl. Math. 49 (1978; Zbl 0432.54007)].
MSC:
54B20 Hyperspaces in general topology
54D05 Connected and locally connected spaces (general aspects)
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