Cofinality in normal almost compact spaces

Abstract

A regular space is said to be a NAC space if, given any pair of disjoint closed subsets, one of them is compact. The standard example of a noncompact NAC space is an ordinal space of uncountable cofinality. The cofinality of an arbitrary noncompact NAC space is defined, and the extent to which cofinality in NAC spaces behaves like cofinality of ordinal spaces is discussed.