Absolute countable compactness of products and topological groups (Q2761036)

First, some closed subspaces of \(X\times Y\) are described that are absolutely countably compact (in the sense of \textit{M. V. Matveev} [Topology Appl. 58, No. 1, 81-92 (1994; Zbl 0801.54021)]). Then it is proved that there is a separable, countably compact T\(_2\)-group that is not absolutely countably compact (if \(2^{\omega}<2^{\omega_1}\) and \(2^{\omega_1}\) is sequentially compact, then the group can be constructed sequentially compact).