Resolvability vs. almost resolvability

István Juhász, Saharon Shelah and Lajos Soukup

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 Juhász, Soukup, and Szentmiklóssy, 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 ${\kappa}$.

Key words and phrases: kappa-resolvable space, almost kappa-resolvable space, extraresolvable space

2000 Mathematics Subject Classification: 54A25, 03E05

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