Resolvability properties via independent families

摘要

The authors give a consistent affirmative response to a question of Juhasz, Soukup and Szentmiklossy: 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 (D(λ))~I is λ-resolvable.