A countably compact free Abelian group whose size has countable cofinality

[EN] Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “k-Lindelöfness” and ”k-compactness” for cardinals k. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result of Som Naimpally, to who this article is hearty dedicated.