# Almost disjoint families and property (a)

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 3, page 229-240
- ISSN: 0016-2736

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topSzeptycki, Paul, and Vaughan, Jerry. "Almost disjoint families and property (a)." Fundamenta Mathematicae 158.3 (1998): 229-240. <http://eudml.org/doc/212313>.

@article{Szeptycki1998,

abstract = {We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < p$ 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 $p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).},

author = {Szeptycki, Paul, Vaughan, Jerry},

journal = {Fundamenta Mathematicae},

keywords = {property (a), density; extent; almost disjoint families; Ψ-space; CH; GCH; Martin's Axiom; $p = c$; Cohen forcing; Q-set; weakly inaccessible cardinal.; property (a); density; almost disjoint family; -space; Martin's axiom},

language = {eng},

number = {3},

pages = {229-240},

title = {Almost disjoint families and property (a)},

url = {http://eudml.org/doc/212313},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Szeptycki, Paul

AU - Vaughan, Jerry

TI - Almost disjoint families and property (a)

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 3

SP - 229

EP - 240

AB - We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < p$ 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 $p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).

LA - eng

KW - property (a), density; extent; almost disjoint families; Ψ-space; CH; GCH; Martin's Axiom; $p = c$; Cohen forcing; Q-set; weakly inaccessible cardinal.; property (a); density; almost disjoint family; -space; Martin's axiom

UR - http://eudml.org/doc/212313

ER -

## References

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- [4] W. G. Fleissner and A. W. Miller, On Q-sets, Proc. Amer. Math. Soc. 78 (1980), 280-284.
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- [9] W. Just, M. V. Matveev and P. J. Szeptycki, Some results on property (a), Topology Appl., to appear. Zbl0944.54014
- [10] K. Kunen, Set Theory, North-Holland, 1980.
- [11] M. V. Matveev, Absolutely countably compact spaces, Topology Appl. 58 (1994), 81-92. Zbl0801.54021
- [12] M. V. Matveev, On feebly compact spaces with property (a), preprint.
- [13] M. V. Matveev, Some questions on property (a), Questions Answers Gen. Topology 15 (1997), 103-111. Zbl1002.54016
- [14] M. E. Rudin, I. Stares and J. E. Vaughan, From countable compactness to absolute countable compactness, Proc. Amer. Math. Soc. 125 (1997), 927-934. Zbl0984.54027

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