A group under \(\text{MA}_{\text{countable}}\) whose square is countably compact but whose cube is not
The author extends the methods from \textit{K. P. Hart} and \textit{J. van Mill} [Trans. Am. Math. Soc. 323, No. 2, 811-821 (1991; Zbl 0770.54037)] to construct an example as stated in the title as well as, for a given finite~\(k\), a family \(\{H_n:n\in\omega\}\) of topological groups such that a finite product \(\prod_{n\in F} H_n\) is countably compact if{f} \(F\)~has at most \(k\)~elements. As in the aforementioned paper the constructions require \(\text{MA}_{\text{countable}}\) to go through. It is still unknown whether there exist, in ZFC, countably compact groups whose product is not countably compact.
scientific article; zbMATH DE number 1307892
scientific article