Countable paracompactness, normality, and Moore spaces

Abstract

In this paper we show that MA + ¬ CH {\text {MA}} + \neg {\text {CH}} implies that there exists a countably paracompact Moore space which is not normal. Further, if there is a model of set theory in which every countably paracompact Moore space is normal, then the normal Moore space conjecture is true in that model. Other examples are given, including a nonnormal space constructed with ⋄ \diamond which is countably compact, T 3 {T_3} , first countable, locally compact, perfect, and hereditarily separable.