| Title:
|
I-weight of compact and locally compact LOTS (English) |
| Author:
|
Bailey, Brad |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
677-688 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Ram'{\i}rez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [{\it A reflection theorem for i-weight\/}, Topology Proc. {\bf 28} (2004), no. 1, 277--281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary and sufficient condition for i-weight to reflect cardinal $\kappa$. (English) |
| Keyword:
|
i-weight |
| Keyword:
|
reflection |
| Keyword:
|
T$_1$-separating weight |
| Keyword:
|
LOTS |
| Keyword:
|
compact |
| MSC:
|
54A05 |
| MSC:
|
54A25 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1199.54029 |
| idMR:
|
MR2375168 |
| . |
| Date available:
|
2009-05-05T17:05:38Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119690 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.Helderman, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[2] Hajnal A., Juhász I.: Having a small weight is determined by the small subspaces.Proc. Amer. Math. Soc. 79 (1980), 4 657-658. MR 0572322 |
| Reference:
|
[3] Hodel R.: Cardinal functions I.in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.1-61. Zbl 0559.54003, MR 0776620 |
| Reference:
|
[4] Hodel R.E., Vaughan J.E.: Reflection theorems for cardinal functions.Topology Appl. 100 (2000), 47-66. Zbl 0943.54003, MR 1731704 |
| Reference:
|
[5] Ramírez-Páramo A.: A reflection theorem for i-weight.Topology Proc. 28 (2004), 1 277-281. Zbl 1079.54005, MR 2105463 |
| Reference:
|
[6] Tkachenko M.G.: Chains and cardinals.Soviet Math. Dokl. 119 (1978), 382-385. Zbl 0404.54002 |
| . |
