Countable compactness of hyperspaces and Ginsburg's questions

Jiling Cao, Tsugunori Nogura and A. H. Tomita


In this paper, we study the countable compactness and pseudocompactness of the
hyperspace $2^X$ of a Hausdorff space $X$ consisting of all nonempty closed
subsets of $X$ equipped with the Vietoris topology. Some open questions posed
by Ginsburg in 1975 are considered. In particular, we give partial solutions
to one of them.

Countably compact, homogeneous, pseudocompact, Vietoris topology

Math Review Classification
Primary 54D20 ; Secondary 03E35, 54B20

Last Updated
13 May, 2003

11 pages

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