We consider the question: when does a Ψ-space satisfy property (a)? We show that if then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).
@article{bwmeta1.element.bwnjournal-article-fmv158i3p229bwm,
author = {Paul Szeptycki and Jerry Vaughan},
title = {Almost disjoint families and property (a)},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {229-240},
zbl = {0933.54005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv158i3p229bwm}
}
Szeptycki, Paul; Vaughan, Jerry. Almost disjoint families and property (a). Fundamenta Mathematicae, Tome 158 (1998) pp. 229-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i3p229bwm/
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