Resolvability properties via independent families |
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Authors: | WW Comfort Wanjun Hu |
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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 |
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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. |
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Keywords: | primary 05A18 03E05 54A10 secondary 03E35 54A25 05D05 |
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