Israel Journal of Mathematics

, Volume 166, Issue 1, pp 1–16 | Cite as

Resolvability and monotone normality

  • István Juhász
  • Lajos Soukup
  • Zoltán Szentmiklóssy
Article

Abstract

A space X is said to be κ-resolvable (resp., almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp., almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable if and only if it is Δ(X)-resolvable, where Δ(X) = min{|G| : G\(\not 0\) open}.

We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = min{2ω, ω2}. On the other hand, if κ is a measurable cardinal then there is a MN space X with Δ(X) = κ such that no subspace of X is ω1-resolvable.

Any MN space of cardinality < ℵω is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space X with |X| = Δ(X) = ℵω such that no subspace of X is ω2-resolvable.

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Copyright information

© Hebrew University Magnes Press 2008

Authors and Affiliations

  • István Juhász
    • 1
  • Lajos Soukup
    • 1
  • Zoltán Szentmiklóssy
    • 2
  1. 1.Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.Department of AnalysisEötvös University of BudapestBudapestHungary

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