Resolvability vs. almost resolvability

Details Resolvability vs. almost resolvability Resolvability vs. almost resolvability

2007-02-11

arxiv.org/abs/math/0702296v1

Mathematics

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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} .

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