Are initially ω1 -compact separable regular spaces compact?
Dow, Alan ; Juhász, Istvan
Fundamenta Mathematicae, Tome 154 (1997), p. 123-132 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:212229 
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     author = {Alan Dow and Istvan Juh\'asz},
     title = {Are initially $$\omega$\_1$ -compact separable regular spaces compact?},
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     volume = {154},
     year = {1997},
     pages = {123-132},
     zbl = {0907.54002},
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Dow, Alan; Juhász, Istvan. Are initially $ω_1$ -compact separable regular spaces compact?. Fundamenta Mathematicae, Tome 154 (1997) pp. 123-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv154i2p123bwm/

[00000] [1] B. Balcar and P. Simon, On minimal π-character of points in extremally disconnected compact spaces, Topology Appl. 41 (1991), 133-145. | Zbl 0752.54013

[00001] [2] Z. Balogh, A. Dow, D. Fremlin, and P. Nyikos, Countable tightness and proper forcing, Bull. Amer. Math. Soc. 19 (1988), 295-298. | Zbl 0661.54007

[00002] [3] M. Bell and K. Kunen, On the π-character of ultrafilters, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 351-356. | Zbl 0475.54001

[00003] [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. | Zbl 0684.54003

[00004] [5] A. Dow, I. Juhász, L. Soukoup and Z. Szentmiklossy, More on sequentially compact implying pseudoradial, Topology Appl. 73 (1996), 191-195. | Zbl 0859.54002

[00005] [6] A. Hajnal and I. Juhász, On hereditarily α-Lindelöf and α-separable spaces, II, Fund. Math. 81 (1974), 147-158.

[00006] [7] I. Juhász, Cardinal functions II, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, 63-109.

[00007] [8] P. Koszmider, Splitting ultrafilters of the thin-very tall algebra and initially ω1-compactness, preprint.

[00008] [9] K. Kunen, Weak P-points in N*, in: Colloq. Math. Soc. János Bolyai, 23, North-Holland, 1980, 741-749.

[00009] [10] M. Rabus, An ω2-minimal Boolean algebra, Trans. Amer. Math. Soc. 348 (1996), 3235-3244. | Zbl 0859.03026

[00010] [11] M. Rajagopalan, A chain compact space which is not strongly scattered, Israel J. Math. 23 (1976), 117-125. | Zbl 0331.54012

[00011] [12] P. Simon, Divergent sequences in bicompacta, Soviet Math. Dokl. 243 (1978), 1573-1577. | Zbl 0415.54004

[00012] [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. | Zbl 0561.54004

[00013] [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.