On nearly paracompact spaces and nearly full normality

Abstract

This paper is a continuation of the study of nearly paracompact spaces, initiated by Singal and Arya in~[5]. After suitably defining the generalized versions of normality and full normality in our setting, we achieve, as our final objective, an analogue of the celebrated theorem of A. H. Stone on paracompactness viz\. "a Hausdorff topological spaces is paracompact iff it is fully normal''. Incidentally, in course of the deliberation, we obtain a few extended forms of certain well known results on paracompactness.