Baire irresolvable spaces with countable Souslin number

Abstract

A topological space X is almost resolvable if X is the union of a countable collection of subsets each of them with empty interior. In this paper we prove that under the Continuum Hypothesis, the existence of a measurable cardinal is equivalent to the existence of a Baire crowded ccc almost irresolvable T1 space. We also prove (1.) Every crowded ccc space with cardinality less than the first weakly inaccessible cardinal is almost resolvable. (2.) If 2ω is less than the first weakly inaccessible cardinal, then every T2 crowded ccc space is almost resolvable.