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Resolvability properties via independent families
Authors:WW Comfort  Wanjun Hu
Affiliation:a Department of Mathematics and Computer Science, Wesleyan University, Wesleyan Station, Middletown, CT 06459, USA
b Department of Mathematics and Computer Science, Albany State University, Albany, GA 31705, USA
Abstract:The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable.
Keywords:primary  05A18  03E05  54A10  secondary  03E35  54A25  05D05
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