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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{2 ω , ω 2}. 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 ω 1-resolvable.

Any MN space of cardinality < ℵ ω is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space X with |X| = Δ(X) = ℵ ω such that no subspace of X is ω 2-resolvable.

Keywords

Normal Space Pairwise Disjoint Dense Subspace Regular Cardinal Measurable Cardinal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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