A pseudocompact group which is not strongly pseudocompact

Abstract

A space X is called strongly pseudocompact if for each sequence (Un)n∈N of pairwise disjoint nonempty open subsets of X there is a sequence (xn)n∈N of points in X such that clX({xn:n∈N})∖(⋃n∈NUn)≠∅ and xn∈Un, for each n∈N. It is evident that every countably compact space is strongly pseudocompact and every strongly pseudocompact space is pseudocompact. In this paper, we construct a pseudocompact group that is not strongly pseudocompact answering two questions posed in [13].