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## Fundamenta Mathematicae

2012 | 217 | 1 | 83-93
Tytuł artykułu

### Ordinal remainders of classical ψ-spaces

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Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain ${T_{α}: α < λ}$ of infinite subsets of ω, there exists $ℳ ⊂ [ω]^{ω}$, an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < 𝔱⁺, where 𝔱 is the tower number, there exists a mod-finite ascending chain ${T_{α}: α < λ}$, hence a ψ-space with Stone-Čech remainder homeomorphic to λ +1. This generalizes a result credited to S. Mrówka by J. Terasawa which states that there is a MADF ℳ such that βψ∖ψ is homeomorphic to ω₁ + 1.
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Tom
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83-93
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2012
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autor
• Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.
autor
• Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, U.S.A.
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