The Scarborough-Stone problem for Hausdorff spaces
\textit{C. T. Scarborough} and \textit{A. H. Stone} [Trans. Am. Math. Soc. 124, 131-147 (1966; Zbl 0151.300)] proved that every product of no more than \(\aleph_ 1\) sequentially compact spaces (no separation axioms assumed) is countably compact. They asked if every product of sequentially compact spaces is countably compact. This is now known as the Scarborough-Stone problem. Previous work has answered the question negatively for the class of completely regular, Hausdorff spaces in many models of set theory. The authors answer the question negatively in ZFC for the class of Hausdorff spaces. They provide two different methods for constructing families of sequentially compact spaces whose product is not countably compact. One of these constructions is a modification of the Ostaszewski technique; the other is an iteration of the \(\Psi\)-space construction.
scientific article; zbMATH DE number 123584