Weak normality properties and countable paracompactness

Abstract

According to P. Nyikos, a topological space is called paranormal, if every countable discrete system of closed sets {Dn:n=1,2,3,...} may be expanded to a locally finite system of open sets {Un:n=1,2,3,...}, i.e. Dn⊂Un for each n and Dm∩Un≠∅ if and only if Dm=Dn. Using the notion of paranormality and δ-normality, we obtain some characteristics of countably paracompact spaces in classes of strongly P-sequential spaces and weakly P-sequential spaces, where P is a nonempty set of free ultrafilters.