Dense minimal pseudocompact subgroups of compact Abelian groups
A Hausdorff topological group \(G\) is pseudocompact if every continuous real-valued function on \(G\) is bounded. Motivated by a noteworthy theorem of \textit{W. W. Comfort} and \textit{J. van Mill} [Proc. Am. Math. Soc. 135, 4039--4044 (2007; Zbl 1138.22002)], which guarantees that a pseudocompact abelian group \(G\) has a proper dense pseudocompact subgroup if and only if \(G\) is non-metrizable, the author studies pseudocompact abelian groups which admit proper dense pseudocompact subgroups satisfying other conditions. In this direction she establishes two results valid in the context of compact abelian groups. First, she obtains necessary and sufficient conditions for such a topological group to admit some proper dense essential pseudocompact subgroup. Second, she obtains necessary and sufficient conditions for such a topological group to admit some proper dense essential subgroup. Some open problems are included in the paper.
scientific article; zbMATH DE number 5365204
scientific article