Weak normality properties and countable paracompactness (Q1985649)

This paper deals with the characterization of countable paracompactness in some class of strongly (resp. weakly) \(\mathcal{P}\)-sequential space by using paranormality (in sense of Nyikos) and \(\delta\)-normality, where \(\mathcal{P}\) is the class of free ultrafilters. Furthermore, the author examines the relationship between countable paracompact and paranormal spaces, and shows that the Cartesian product of uncountably many copies of \(N\) is not paranormal which eventually generalizes the results of \textit{A. H. Stone} [Bull. Am. Math. Soc. 54, 977--982 (1948; Zbl 0032.31403)] and \textit{K. Nagami} [Fundam. Math. 73, 261--270 (1972; Zbl 0226.54005)], respectively, where \(N\) is a countable discrete topological space.