Resolvability vs. almost resolvability

Abstract

A space X is kappa-resolvable (resp. almost kappa-resolvable) if it contains kappa dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhasz, Soukup, and Szentmiklossy, and improving a consistency result of Comfort and Hu, we prove, in ZFC, that for every infinite cardinal {kappa} there is an almost 2^{kappa}-resolvable but not {omega}_1-resolvable space of dispersion character {kappa} .