Normality and countable paracompactness of products with \(\sigma\)-spaces having special nets (Q1295283)

A well-known result by Morita-Rudin-Starbird [\textit{M. E. Rudin}, \textit{M. Starbird}, General Topol. Appl. 5, 235-248 (1975; Zbl 0305.54010)] states the equivalence of the properties of normality and countable paracompactness of the product \(X\times Y\) where \(X\) is countably paracompact and normal, and \(Y\) is metrizable. There are known also some modifications of this result (see e.g. [\textit{N. Zhong}, Topology Appl. 45, No. 2, 131-144 (1992; Zbl 0780.54006)]). Investigating the problem of possible generalizations of this result the authors introduce and study some subclasses of the class of \(\sigma\)-spaces in the sense of Okuyama. The smallest one of these classes, the so-called \(LF\)-netted spaces, contain all \(F_\sigma\)-discrete spaces as well as all stratifiable \(F_\sigma\)-metrizable spaces. The main result of the paper establishes the equivalence of the properties of normality and countable paracompactness of the product of a paracompact \(LF\)-netted space with a countably paracompact normal space.