Ordinal remainders of classical ψ-spaces

• Autorzy: Alan Dow , Jerry E. Vaughan
• Języki publikacji: EN

Abstrakty

EN

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.

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.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 217
• Numer: 1
• Strony: 83-93

Daty

wydano

2012

Twórcy

autor

Alan Dow

• Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.

autor

Jerry E. Vaughan

• Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, U.S.A.

Identyfikatory

DOI

10.4064/fm217-1-7