| Title:
|
A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom (English) |
| Author:
|
Bell, Murray |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
589-594 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every compact ccc space of countable $\pi$-character is separable. The space constructed has the additional property that it does not map continuously onto $I^{\omega_1}$. (English) |
| Keyword:
|
ccc |
| Keyword:
|
non-separable |
| Keyword:
|
Hausdorff gap |
| Keyword:
|
$\pi$-character |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54D30 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 0881.54004 |
| idMR:
|
MR1426923 |
| . |
| Date available:
|
2009-01-08T18:26:22Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118865 |
| . |
| Reference:
|
[Ba84] Baumgartner J.E.: Applications of the Proper Forcing Axiom.Handbook of Set-Theoretic Topology, editors K.Kunen and J.Vaughan, North-Holland, 1984, pp. 913-959. Zbl 0556.03040, MR 0776640 |
| Reference:
|
[Be80] Bell M.: Compact ccc non-separable spaces of small weight.Topology Proceedings 5 (1980), 11-25. MR 0624458 |
| Reference:
|
[Be88] Bell M: $G_\kappa$ subspaces of hyadic spaces.Proc. Amer. Math. Soc. 104 , No.2 (1988), 635-640. MR 0962841 |
| Reference:
|
[Be89] Bell M.: Spaces of Ideals of Partial Functions.Set Theory and its Applications, Lecture Notes in Mathematics 1401, Springer-Verlag, 1989, pp. 1-4. Zbl 0683.54013, MR 1031761 |
| Reference:
|
[Fr84] Fremlin D.H.: Consequences of Martin's Axiom.Cambridge Tracts in Mathematics 84, Cambridge University Press, 1984. Zbl 1156.03050 |
| Reference:
|
[Ju71] Juhasz I.: Cardinal Functions in Topology.Mathematical Centre Tracts 34, Mathematisch Centrum, Amsterdam, 1971. Zbl 0479.54001, MR 0340021 |
| Reference:
|
[Ju77] Juhasz I.: Consistency Results in Topology.Handbook of Mathematical Logic, editor J.Barwise, North-Holland, 1977, pp. 503-522. Zbl 0257.54003 |
| Reference:
|
[Sh72] Shapirovskii B.: On separability and metrizability of spaces with Souslin condition.Soviet Math. Dokl. 13 (1972), 1633-1637. |
| Reference:
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[Sh80] Shapirovskii B.: Maps onto Tikhonov cubes.Russ. Math. Surv. 35.3 (1980), 145-156. |
| Reference:
|
[Sh93] Shapirovskii B. (presented by P.Nyikos and J.Vaughan): The Equivalence of Sequential Compactness and Pseudoradialness in the Class of Compact $T_2$ Spaces, Assuming CH.Papers on General Topology and Applications, Annals of the New York Academy of Sciences 704, 1993, pp. 322-327. MR 1277868 |
| Reference:
|
[To89] Todorcevic S.: Partition Problems in Topology.Contemporary Mathematics 84, American Mathematical Society, Providence, Rhode Island, 1989. Zbl 0659.54001, MR 0980949 |
| Reference:
|
[TF95] Todorcevic S., Farah I.: Some Applications of the Method of Forcing.Yenisey Publ. Co., Moscow, 1995. Zbl 1089.03500, MR 1486583 |
| . |
