| Title:
|
Forcing countable networks for spaces satisfying $\operatorname{R}(X^\omega)=\omega$ (English) |
| Author:
|
Juhász, I. |
| Author:
|
Soukup, L. |
| Author:
|
Szentmiklóssy, Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
159-170 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that all finite powers of a Hausdorff space $X$ do not contain uncountable weakly separated subspaces iff there is a c.c.c poset $P$ such that in $V^P$ $\,X$ is a countable union of $0$-dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of $X$. (English) |
| Keyword:
|
net weight |
| Keyword:
|
weakly separated |
| Keyword:
|
Martin's Axiom |
| Keyword:
|
forcing |
| MSC:
|
03E35 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| idZBL:
|
Zbl 0862.54003 |
| idMR:
|
MR1396168 |
| . |
| Date available:
|
2009-01-08T18:22:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118820 |
| . |
| Reference:
|
[1] Ciesielski K.: On the netweigth of subspaces.Fund. Math. 117 (1983), 1 37-46. MR 0712211 |
| Reference:
|
[2] Hajnal A., Juhász I.: Weakly separated subspaces and networks.Logic '78, Studies in Logic, 97, 235-245. MR 0567672 |
| Reference:
|
[3] Jech T.: Set Theory.Academic Press, New York, 1978. Zbl 1007.03002, MR 0506523 |
| Reference:
|
[4] Juhász I.: Cardinal Functions - Ten Years Later.Math. Center Tracts 123, Amsterdam, 1980. MR 0576927 |
| Reference:
|
[5] Juhász I., Soukup L., Szentmiklóssy Z.: What makes a space have large weight?.Topology and its Applications 57 (1994), 271-285. MR 1278028 |
| Reference:
|
[6] Shelah S.: private communication.. |
| Reference:
|
[7] Tkačenko M.G.: Chains and cardinals.Dokl. Akad. Nauk. SSSR 239 (1978), 3 546-549. MR 0500798 |
| Reference:
|
[8] Todorčevič S.: Partition Problems in Topology.Contemporary Mathematics, vol. 84, Providence, 1989. MR 0980949 |
| . |
