Concerning countable paracompactness and pseudo normality in topological spaces

This paper extends the results of several mathematicians, notably Professor C. H. Dowker, Phillip Zenor, and John Mack, in the study of countably paracompact spaces. The concept of open set summability is introduced and the following theorem is proved. THEOREM. A space is perfectly normal if, and only if, it is both countably paracompact and open set summable. Also included in this paper is an example of a pseudo-normal, non-normal screenable Moore space.