Are initially ω 1 -compact separable regular spaces compact?

Alan Dow; Istvan Juhász

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 2, page 123-132
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Dow, Alan, and Juhász, Istvan. "Are initially $ω_1$ -compact separable regular spaces compact?." Fundamenta Mathematicae 154.2 (1997): 123-132. <http://eudml.org/doc/212229>.

@article{Dow1997,
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.},
author = {Dow, Alan, Juhász, Istvan},
journal = {Fundamenta Mathematicae},
keywords = {regular; separable; initially -compact; Cohen reals},
language = {eng},
number = {2},
pages = {123-132},
title = {Are initially $ω_1$ -compact separable regular spaces compact?},
url = {http://eudml.org/doc/212229},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Dow, Alan
AU - Juhász, Istvan
TI - Are initially $ω_1$ -compact separable regular spaces compact?
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 2
SP - 123
EP - 132
AB - 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.
LA - eng
KW - regular; separable; initially -compact; Cohen reals
UR - http://eudml.org/doc/212229
ER -

References

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  1. [1] B. Balcar and P. Simon, On minimal π-character of points in extremally disconnected compact spaces, Topology Appl. 41 (1991), 133-145. Zbl0752.54013
  2. [2] Z. Balogh, A. Dow, D. Fremlin, and P. Nyikos, Countable tightness and proper forcing, Bull. Amer. Math. Soc. 19 (1988), 295-298. Zbl0661.54007
  3. [3] M. Bell and K. Kunen, On the π-character of ultrafilters, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 351-356. Zbl0475.54001
  4. [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. Zbl0684.54003
  5. [5] A. Dow, I. Juhász, L. Soukoup and Z. Szentmiklossy, More on sequentially compact implying pseudoradial, Topology Appl. 73 (1996), 191-195. Zbl0859.54002
  6. [6] A. Hajnal and I. Juhász, On hereditarily α-Lindelöf and α-separable spaces, II, Fund. Math. 81 (1974), 147-158. 
  7. [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. [8] P. Koszmider, Splitting ultrafilters of the thin-very tall algebra and initially ω 1 -compactness, preprint. 
  9. [9] K. Kunen, Weak P-points in N*, in: Colloq. Math. Soc. János Bolyai, 23, North-Holland, 1980, 741-749. 
  10. [10] M. Rabus, An ω 2 -minimal Boolean algebra, Trans. Amer. Math. Soc. 348 (1996), 3235-3244. Zbl0859.03026
  11. [11] M. Rajagopalan, A chain compact space which is not strongly scattered, Israel J. Math. 23 (1976), 117-125. Zbl0331.54012
  12. [12] P. Simon, Divergent sequences in bicompacta, Soviet Math. Dokl. 243 (1978), 1573-1577. Zbl0415.54004
  13. [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. Zbl0561.54004
  14. [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. 

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