2022-01-262022-01-26197313683995https://hdl.handle.net/10657/8615This 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.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital