| Title:
|
Compactifications and uniformities on sigma frames (English) |
| Author:
|
Walters, Joanne |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
189-198 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A bijective correspondence between strong inclusions and compactifications in the setting of $\sigma$-frames is presented. The category of uniform $\sigma$-frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the $\sigma$-frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined. (English) |
| Keyword:
|
strong inclusion |
| Keyword:
|
compactification |
| Keyword:
|
uniform $\sigma$-frame |
| Keyword:
|
uniform cozero |
| MSC:
|
18B35 |
| MSC:
|
54D35 |
| MSC:
|
54E05 |
| MSC:
|
54E52 |
| MSC:
|
54J05 |
| idZBL:
|
Zbl 0735.54014 |
| idMR:
|
MR1118301 |
| . |
| Date available:
|
2008-10-09T13:11:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116954 |
| . |
| Reference:
|
[1] Banaschewski B.: Frames and compactifications.Proc. I. International Symp. on Extension Theory of Topological Structures and Its Applications. VEB Deutscher Verlag der Wissenschaften, 1969. Zbl 0188.28006 |
| Reference:
|
[2] Banaschewski B., Gilmour C.R.A.: Stone-Čech compactification and dimension theory for regular $\sigma$-frames.J. London Math. Soc.(2) No. 127, 39, part 1 1-8 (1989). Zbl 0675.06005, MR 0989914 |
| Reference:
|
[3] Banaschewski B., Mulvey C.: Stone-Čech compactification of Locales I..Houston J. of Math. 6, 3 (1980), 301-312. Zbl 0473.54026, MR 0597771 |
| Reference:
|
[4] Frith J.L.: The Category of Uniform Frames.Cahier de Topologie et Geometrie, to appear. Zbl 0738.18002, MR 1109372 |
| Reference:
|
[5] Gilmour C.R.A.: Realcompact Alexandroff spaces and regular $\sigma$-frames.Math. Proc. Cambridge Philos. Soc. 96 (1984), 73-79. MR 0743702 |
| Reference:
|
[6] Ginsburg S., Isbell J.R.: Some operators on uniform spaces.Trans. Amer. Math. Soc. 36 (1959), 145-168. Zbl 0087.37601, MR 0112119 |
| Reference:
|
[7] Johnstone P.T.: Stone Spaces.Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[8] Madden J., Vermeer H.: Lindelöf locales and realcompactness.Math. Proc. Camb. Phil. Soc. (1985), 1-8. |
| Reference:
|
[9] Pultr A.: Pointless uniformities I. Complete regularity.Comment. Math. Univ. Carolinae 25 (1984), 91-104. Zbl 0543.54023, MR 0749118 |
| . |
