| Title:
|
In search for Lindelöf $C_p$'s (English) |
| Author:
|
Buzyakova, Raushan Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
145-151 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_p(X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_p(X)$ is less than the Lindelöf number of $C_p(X)$. This example answers negatively Reznichenko's question whether Baturov's theorem holds for countably compact spaces. (English) |
| Keyword:
|
$C_p(X)$ |
| Keyword:
|
space of ordinals |
| Keyword:
|
Lindelöf space |
| MSC:
|
54C35 |
| MSC:
|
54D20 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1098.54010 |
| idMR:
|
MR2076866 |
| . |
| Date available:
|
2009-05-05T16:43:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119443 |
| . |
| Reference:
|
[ARH] Arhangelskii A.: Topological Function Spaces.Math. Appl., vol. 78, Kluwer Academic Publisher, Dordrecht, 1992. MR 1144519 |
| Reference:
|
[ASA] Asanov M.O.: On cardinal invariants of function spaces.Modern Topology and Set Theory, Igevsk, (2), 1979, 8-12. |
| Reference:
|
[BAT] Baturov D.: On subspaces of function spaces.Vestnik MGU, Mat. Mech. 4 (1987), 66-69. Zbl 0665.54004, MR 0913076 |
| Reference:
|
[BUZ] Buzyakova R.: Hereditary D-property of Function Spaces Over Compacta.submitted to Proc. Amer. Math. Soc. Zbl 1064.54029, MR 2073321 |
| Reference:
|
[DOU] van Douwen E.K.: Simultaneous extension of continuous functions.Thesis, Free University, Amsterdam, 1975. |
| Reference:
|
[ENG] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[NAH] Nahmanson L.B.: Lindelöfness in function spaces.Fifth Teraspol Symposium on Topology and its Applications, Kishinev, 1985, p.183. |
| . |
