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Arcwise connectedness of the complement in a hyperspace - MaRDI portal

Arcwise connectedness of the complement in a hyperspace (Q1375807)

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scientific article; zbMATH DE number 1102957
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Arcwise connectedness of the complement in a hyperspace
scientific article; zbMATH DE number 1102957

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    Arcwise connectedness of the complement in a hyperspace (English)
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    22 February 1998
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    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 \textit{S. B. Nadler jun.} [Hyperspaces of sets, Monogr. Textb. Pure Appl. Math. 49 (1978; Zbl 0432.54007)].
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    arcwise connectivity
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