Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
- 46E15: Banach spaces of continuous, differentiable or analytic functions
- 03E17: Cardinal characteristics of the continuum
- 03E25: Axiom of choice and related propositions
- 54C30: Real-valued functions
- 54G12: Scattered spaces
- 03E35: Consistency and independence results
- 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
- 54D80: Special constructions of spaces (spaces of ultrafilters, etc.)
Czasopismo
Rocznik
Tom
Numer
Strony
83-93
Opis fizyczny
Daty
wydano
2012
Twórcy
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.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-1-7