Resolvability vs. almost resolvability

2007/02/11 by István Juhász, Saharon Shelah, Juhasz, Istvan +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0702296

openalex publication_date 2007/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 omega₁-resolvable space of dispersion character kappa .

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