Vietoris continuous selections and disconnectedness-like properties

Gutev, Valentin; Nogura, Tsugunori

doi:10.1090/S0002-9939-01-05883-X

Vietoris continuous selections and disconnectedness-like properties
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by Valentin Gutev and Tsugunori Nogura PDF

Proc. Amer. Math. Soc. 129 (2001), 2809-2815 Request permission

Abstract:

Suppose that $X$ is a Hausdorff space such that its Vietoris hyperspace $({\mathcal {F}}(X),\tau _{V})$ has a continuous selection. Do disconnectedness-like properties of $X$ depend on the variety of continuous selections for $({\mathcal {F}}(X),\tau _{V})$ and vice versa? In general, the answer is “yes” and, in some particular situations, we were also able to set proper characterizations.

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