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1993 | 143 | 3 | 221-230
Tytuł artykułu

Countably metacompact spaces in the constructible universe

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EN
Abstrakty
EN
We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a $G_δ$. In addition some nonperfect spaces with σ-disjoint bases are constructed.
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Twórcy
  • Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2M3
  • Department of Mathematics, Ohio University, Athens, Ohio 45701-2979, U.S.A.
Bibliografia
  • [B] D. K. Burke, PMEA and first countable countably metacompact spaces, Proc. Amer. Math. Soc. 92 (1984), 455-460.
  • [C] J. Chaber, Metacompactness and the class of MOBI, Fund. Math. 91 (1976), 211-217.
  • [D] P. Davies, Nonperfect space with point-countable bases, Proc. Amer. Math. Soc. 77 (1979), 276-278.
  • [vD] E. K. van Douwen, The integers and topology, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 111-167.
  • [DTW] A. Dow, F. D. Tall and W. A. R. Weiss, New proofs of the consistency of the normal Moore space conjecture I, Topology Appl. 37 (1990), 33-51.
  • [F] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298.
  • [FR] W. G. Fleissner and M. Reed, Paralindelöf spaces and spaces with a σ-locally countable base, Topology Proc. 2 (1977), 89-110.
  • [K] K. Kunen, Set Theory, An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980.
  • [N1] P. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), 429-435.
  • [N2] P. Nyikos, Countably metacompact, locally countable spaces in the constructible universe, Topology Appl., to appear.
  • [S] P. J. Szeptycki, Uncovering separation properties in the Easton model, preprint.
  • [T1] F. D. Tall, Set-theoretic consistence results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. 148 (1977).
  • [T2] F. D. Tall, Covering and separation properties in the Easton model, Topology Appl. 28 (1988), 155-163.
  • [W] S. Watson, Separation in countably paracompact spaces, Trans. Amer. Math. Soc. 290 (1985), 831-842.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv143i3p221bwm
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