Inequality and equality for the extent of products with a special factor - Hirata, Yasushi; Yajima, Yukinobu (Topology Proceedings, 2021)
For a space $X$, let $e(X)=\sup \{|D|: D$ is a closed discrete subset in $X\} · ω$, which is called the extent of $X$. First, we give some examples of a rectangular product $X × Y$ with $e(X × Y)> e(X) · e(Y)=ω$. Secondly, we give an equivalent condition for a given space $X$ such that $e(X × Y)>e(X) · e(Y)$ for a certain special factor $Y$. Finally, we discuss when $e(X × Y)=e(X) · e(Y)$ for a product $X × Y$ with a special factor $X$.