Countable compactness of hyperspaces and Ginsburgʹs questions

In this paper, we study the countable compactness and pseudocompactness of the hyperspace 2X 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.