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)={|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.