LAUSR

Abstract According to P. Nyikos, a topological space is called paranormal, if every countable discrete system of closed sets { D n : n = 1 , 2 , 3 , . . . } may be expanded to a locally finite system of open sets { U n : n = 1 , 2 , 3 , . . . } , i.e. D n ⊂ U n for each n and D m ∩ U n ≠ ∅ if and only if D m = D n . 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.