Normality and countable paracompactness of products with σ-spaces having special nets

We introduce and study several subclasses of the class of σ-spaces. The smallest of the classes considered, that of LF-netted spaces, contains all Fσ-discrete spaces and all stratifiable Fσ-metrizable spaces. The main result of the paper establishes the equivalence of normality and countable paracompactness of the product of an LF-netted space with a countably paracompact and normal space.