| Title:
|
Realcompactification of frames (English) |
| Author:
|
Marcus, Nizar |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
347-356 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a construction of Wallman-type realcompactifications of a frame $L$ by considering regular sub $\sigma$-frames the join of which generates $L$. In particular, we show that the largest such regular sub $\sigma$-frame gives rise to the universal realcompactification of $L$. (English) |
| Keyword:
|
frame |
| Keyword:
|
$\sigma$-frame |
| Keyword:
|
realcompactification |
| MSC:
|
18A99 |
| MSC:
|
18D35 |
| MSC:
|
54D20 |
| MSC:
|
54D35 |
| MSC:
|
54D52 |
| MSC:
|
54D60 |
| MSC:
|
54J05 |
| idZBL:
|
Zbl 0840.54027 |
| idMR:
|
MR1357534 |
| . |
| Date available:
|
2009-01-08T18:18:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118761 |
| . |
| Reference:
|
[1] Banaschewski B., Gilmour C.R.A.: Stone-Čech compactification and dimension theory for regular $\sigma$-frames.J. London Math. Soc. 39 (1989), 1-8. Zbl 0675.06005, MR 0989914 |
| Reference:
|
[2] Gilmour C.R.A.: Realcompactifications through zero-set spaces.Quaestiones Math. 6 (1983), 73-95. Zbl 0521.54012, MR 0700241 |
| Reference:
|
[3] Gilmour C.R.A.: Realcompact spaces and regular $\sigma$-frames.Math. Proc. Camb. Phil. Soc. 96 (1984), 73-79. Zbl 0547.54021, MR 0743702 |
| Reference:
|
[4] Johnstone P.T.: Stone Spaces.Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[5] Madden J., Vermeer J.: Lindelöf locales and realcompactness.Math. Proc. Camb. Phil. Soc. 99 (1986), 473-480. Zbl 0603.54021, MR 0830360 |
| Reference:
|
[6] G. Schlitt: ${\Bbb N}$-Compact frames and applications.Doctoral thesis, McMaster University, 1990. MR 1118300 |
| . |
