On properties of countable paracompactness type in products (Q1584152)

The application of the known characteristics of the countably paracompact spaces involves a new class of \(\omega\)-countably paracompact spaces. It is proved that the pseudonormal spaces are \(\omega\)-countably paracompact. The author proves the analogues of the known theorems of \textit{M.~Katětov} [Fundam. Math. 35, 271-274 (1948; Zbl 0031.28301)]\ and of \textit{P.~Zenor} [Proc. Am. Math. Soc. 30, No. 1, 199-201 (1971; Zbl 0222.54025)]\ on hereditary normality and hereditary countable paracompactness of products. The conditions are established under which the \(\omega\)-countable compactness of \(F_\sigma\)-subsets of \(X^2\smallsetminus\Delta\) implies the pseudocharacter countability of the points of space~\(X\).