Three examples of pseudocompact quasitopological groups
It is known that the product of an arbitrary family of pseudocompact topological groups is pseudocompact and both a topological group of countable cellularity and a pseudocompact topological group are Moscow spaces, where a space \(X\) is called \textit{Moscow} if the closure of every open subset of \(X\) is the union of a family of \(G_{\delta}\)-sets in \(X\). In this paper, the authors show that the above results for topological groups cannot be extended to quasitopological groups. Indeed, they show that there exist two pseudocompact quasitopological groups whose product is not pseudocompact and a pseudocompact quasitopological group of countable cellularity such that it is not Moscow.
scientific article; zbMATH DE number 5083225