A Tale of Two (s)-ities

Abstract

In the product $X\times Y$ of two uncountable complete separable metric spaces, not every $(s)$-set belongs to the $\sigma$-algebra generated by the products of $(s)$-sets in $X$ with $(s)$-sets in~$Y$. The construction makes use of the fact that the Boolean algebra $(s)/(s_0)$ is complete.