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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)
##### Keywords:
arcwise connectivity
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