# Are initially ${\omega}_{1}$ -compact separable regular spaces compact?

Fundamenta Mathematicae (1997)

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

## Access Full Article

top## Abstract

top## How to cite

topDow, 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

top- [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] 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] 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] 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] A. Dow, I. Juhász, L. Soukoup and Z. Szentmiklossy, More on sequentially compact implying pseudoradial, Topology Appl. 73 (1996), 191-195. Zbl0859.54002
- [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 ${\omega}_{1}$-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 ${\omega}_{2}$-minimal Boolean algebra, Trans. Amer. Math. Soc. 348 (1996), 3235-3244. Zbl0859.03026
- [11] M. Rajagopalan, A chain compact space which is not strongly scattered, Israel J. Math. 23 (1976), 117-125. Zbl0331.54012
- [12] P. Simon, Divergent sequences in bicompacta, Soviet Math. Dokl. 243 (1978), 1573-1577. Zbl0415.54004
- [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] 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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.