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1998 | 158 | 3 | 229-240
Tytuł artykułu

Almost disjoint families and property (a)

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EN
Abstrakty
EN
We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < \got p$ 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 $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).
Twórcy
  • Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, North Carolina 27412, U.S.A., vaughanj@steffi.uncg.edu
Bibliografia
  • [1] M. G. Bell, On the combinatorial principal P(c), Fund. Math. 114 (1981), 149-157.
  • [2] E. K. van Douwen, The integers and topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 111-167.
  • [3] R. Engelking, General Topology, PWN, Warszawa, 1977.
  • [4] W. G. Fleissner and A. W. Miller, On Q-sets, Proc. Amer. Math. Soc. 78 (1980), 280-284.
  • [5] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
  • [6] L. Gillman and M. Jerison, Rings of Continuous Functions, van Nostrand, Princeton, 1960.
  • [7] S. H. Hechler, Short complete nested sequences in βN\N and small maximal almost-disjoint families, Gen. Topology Appl. 2 (1972), 139-149.
  • [8] R. E. Hodel, Cardinal Functions I, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 1-61.
  • [9] W. Just, M. V. Matveev and P. J. Szeptycki, Some results on property (a), Topology Appl., to appear.
  • [10] K. Kunen, Set Theory, North-Holland, 1980.
  • [11] M. V. Matveev, Absolutely countably compact spaces, Topology Appl. 58 (1994), 81-92.
  • [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.
  • [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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv158i3p229bwm
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