Download PDF - Are initially $ω_1$ -compact separable regular spaces compact?All rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Are initially ω1 -compact separable regular spaces compact?

Authors 1, 2

Affiliations

  1. Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3
  2. Mathematical Institute, Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary

Abstract

We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.

Bibliography

  1. B. Balcar and P. Simon, On minimal π-character of points in extremally disconnected compact spaces, Topology Appl. 41 (1991), 133-145.
  2. Z. Balogh, A. Dow, D. Fremlin, and P. Nyikos, Countable tightness and proper forcing, Bull. Amer. Math. Soc. 19 (1988), 295-298.
  3. M. Bell and K. Kunen, On the π-character of ultrafilters, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 351-356.
  4. A. Dow, Compact spaces of countable tightness in the Cohen model, in: J. Steprāns and S. Watson (eds.), Set Theory and its Applications, Lecture Notes in Math. 1401, Springer, 1989, 55-67.
  5. A. Dow, I. Juhász, L. Soukoup and Z. Szentmiklossy, More on sequentially compact implying pseudoradial, Topology Appl. 73 (1996), 191-195.
  6. A. Hajnal and I. Juhász, On hereditarily α-Lindelöf and α-separable spaces, II, Fund. Math. 81 (1974), 147-158.
  7. I. Juhász, Cardinal functions II, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 63-109.
  8. P. Koszmider, Splitting ultrafilters of the thin-very tall algebra and initially ω1-compactness, preprint.
  9. K. Kunen, Weak P-points in N*, in: Colloq. Math. Soc. János Bolyai, 23, North-Holland, 1980, 741-749.
  10. M. Rabus, An ω2-minimal Boolean algebra, Trans. Amer. Math. Soc. 348 (1996), 3235-3244.
  11. M. Rajagopalan, A chain compact space which is not strongly scattered, Israel J. Math. 23 (1976), 117-125.
  12. P. Simon, Divergent sequences in bicompacta, Soviet Math. Dokl. 243 (1978), 1573-1577.
  13. E. K. van Douwen, The integers and topology, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 111-168.
  14. J. Vaughan, Countably compact and sequentially compact spaces, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 569-601.
Fundamenta Mathematicae
1997/154/2
Export to PBN, Opens in new tab
Pages:
123-132
Main language of publication
English
Received
1996-08-29
Accepted
1996-12-18
Published
1997
Exact and natural sciences