Versions of normality and some weak forms of the axiom of choice. preprint

Abstract. We investigate the set theoretical strength of some properties of normality, including Urysohn’s Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of Fσ subsets of normal spaces. Introduction. The notion of a normal topological space has been of interest to topologists for many years. (See, for example, [2], [4], [7], [12], [13], [18], and [20].) In [4] it has been shown that there exists a close connection between properties of normality and the axiom of choice. In particular, in [4], van Douwen established that the proposition: “The disjoint union of a family X = {Xn: n ∈ ω} of orderable topological spaces such that each X