| Title:
|
On almost discrete space (English) |
| Author:
|
Estaji, Ali Akbar |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
69-76 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $C(X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C(X)$. The intersection of essential weak ideal in $C(X)$ is also studied. (English) |
| Keyword:
|
essential weak ideal |
| Keyword:
|
weak socle |
| Keyword:
|
minimal ideal |
| Keyword:
|
almost discrete space |
| Keyword:
|
scattered space |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
realcompactification |
| MSC:
|
13A30 |
| MSC:
|
54C40 |
| idZBL:
|
Zbl 1212.54056 |
| idMR:
|
MR2431232 |
| . |
| Date available:
|
2008-06-06T22:52:49Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108097 |
| . |
| Reference:
|
[1] Azarpanah, F.: Essential ideals in $C(X)$.Period. Math. Hungar. 3 (12) (1995), 105–112. Zbl 0869.54021, MR 1609417, 10.1007/BF01876485 |
| Reference:
|
[2] Azarpanah, F.: Intersection of essential ideals in $C(X)$.Proc. Amer. Math. Soc. 125 (7) (1997), 2149–2154. Zbl 0867.54023, MR 1422843, 10.1090/S0002-9939-97-04086-0 |
| Reference:
|
[3] Dietrich, W.: On the ideals in $C(X)$.Trans. Amer. Math. Soc. 152 (1970), 61–77. MR 0265941, 10.1090/S0002-9947-1970-0265941-2 |
| Reference:
|
[4] Gillman, L., Jerison, M.: Rings of continuous functions.Springer-Verlag, 1979. MR 0407579 |
| Reference:
|
[5] Goodearl, K. R.: Von Neumann regular rings.Pitman, San Francisco, 1979. Zbl 0411.16007, MR 0533669 |
| Reference:
|
[6] Henriksen, M., Wilson, R. G.: Almost discrete SV-space.Topology Appl. 46 (1992), 89–99. Zbl 0791.54049, MR 1184107, 10.1016/0166-8641(92)90123-H |
| Reference:
|
[7] Karamzadeh, O. A. S., Rostami, M.: On the intrinsic topology and some related ideals of $C(X)$.Proc. Amer. Math. Soc. 93 (1985), 179–184. Zbl 0524.54013, MR 0766552 |
| Reference:
|
[8] Zand, M. R. Ahmadi: Strongly Blumberg space.5th Annual Iranian Math. Conf. January 26–29, Ahvaz, Iran, 2005. |
| Reference:
|
[9] Zand, M. R. Ahmadi: Strongly Blumberg space.Ph.D. thesis, Shahid Chamran University of Ahvaz in Iran, 2006. |
| . |
