Ordinal remainders of classical ψ-spaces

Alan Dow, and Jerry E. Vaughan. "Ordinal remainders of classical ψ-spaces." Fundamenta Mathematicae 217.1 (2012): 83-93. <http://eudml.org/doc/283311>.

@article{AlanDow2012,
abstract = {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 < ⁺, where 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.},
author = {Alan Dow, Jerry E. Vaughan},
journal = {Fundamenta Mathematicae},
keywords = {cardinal number; ordinal; almost disjoint family (ADF); maximal ADF; Stone-Čech compactification; Stone-Čech remainder; ZFC},
language = {eng},
number = {1},
pages = {83-93},
title = {Ordinal remainders of classical ψ-spaces},
url = {http://eudml.org/doc/283311},
volume = {217},
year = {2012},
}

TY - JOUR
AU - Alan Dow
AU - Jerry E. Vaughan
TI - Ordinal remainders of classical ψ-spaces
JO - Fundamenta Mathematicae
PY - 2012
VL - 217
IS - 1
SP - 83
EP - 93
AB - 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 < ⁺, where 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.
LA - eng
KW - cardinal number; ordinal; almost disjoint family (ADF); maximal ADF; Stone-Čech compactification; Stone-Čech remainder; ZFC
UR - http://eudml.org/doc/283311
ER -