ArticleOriginal scientific text

Title

Countably metacompact spaces in the constructible universe

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2M3
  2. Department of Mathematics, Ohio University, Athens, Ohio 45701-2979, U.S.A.

Abstract

We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a Gδ. In addition some nonperfect spaces with σ-disjoint bases are constructed.

Keywords

countably metacompact, Gδ, ♢*

Bibliography

  1. [B] D. K. Burke, PMEA and first countable countably metacompact spaces, Proc. Amer. Math. Soc. 92 (1984), 455-460.
  2. [C] J. Chaber, Metacompactness and the class of MOBI, Fund. Math. 91 (1976), 211-217.
  3. [D] P. Davies, Nonperfect space with point-countable bases, Proc. Amer. Math. Soc. 77 (1979), 276-278.
  4. [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.
  5. [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.
  6. [F] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298.
  7. [FR] W. G. Fleissner and M. Reed, Paralindelöf spaces and spaces with a σ-locally countable base, Topology Proc. 2 (1977), 89-110.
  8. [K] K. Kunen, Set Theory, An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980.
  9. [N1] P. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), 429-435.
  10. [N2] P. Nyikos, Countably metacompact, locally countable spaces in the constructible universe, Topology Appl., to appear.
  11. [S] P. J. Szeptycki, Uncovering separation properties in the Easton model, preprint.
  12. [T1] F. D. Tall, Set-theoretic consistence results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. 148 (1977).
  13. [T2] F. D. Tall, Covering and separation properties in the Easton model, Topology Appl. 28 (1988), 155-163.
  14. [W] S. Watson, Separation in countably paracompact spaces, Trans. Amer. Math. Soc. 290 (1985), 831-842.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14334.pdf

Pages:
221-230
Main language of publication
English
Received
1992-09-11
Accepted
1993-03-25
Published
1993
Exact and natural sciences