| Title:
|
On the completeness of localic groups (English) |
| Author:
|
Banaschewski, B. |
| Author:
|
Vermeulen, J. J. C. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
293-307 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main purpose of this paper is to show that any localic group is complete in its two-sided uniformity, settling a problem open since work began in this area a decade ago. In addition, a number of other results are established, providing in particular a new functor from topological to localic groups and an alternative characterization of $LT$-groups. (English) |
| Keyword:
|
localic group |
| Keyword:
|
Closed Subgroup Theorem for localic groups |
| Keyword:
|
the uniformities of a localic group |
| Keyword:
|
two-sidedly complete topological groups |
| Keyword:
|
$LT$-groups |
| MSC:
|
18D35 |
| MSC:
|
22A05 |
| MSC:
|
54E15 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0981.18010 |
| idMR:
|
MR1732650 |
| . |
| Date available:
|
2009-01-08T18:52:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119085 |
| . |
| Reference:
|
[1] Banaschewski B.: Completion in Pointfree Topology.Lecture Notes in Mathematics and Applied Mathematics No. 2/96, University of Cape Town, 1996. Zbl 1034.06008 |
| Reference:
|
[2] Banaschewski B., Hong S.S., Pultr A.: On the completion of nearness frames.Quaest. Math. 21 (1998), 19-37. Zbl 0931.54025, MR 1658467 |
| Reference:
|
[3] Bourbaki N.: General Topology.Herrman, Paris and Addison-Wesley, Reading, Massachusetts, 1966. Zbl 1107.54001 |
| Reference:
|
[4] Isbell J.R.: Uniform spaces.A.M.S. Mathematical Survey 12, Providence, Rhode Island, 1964. Zbl 0124.15601, MR 0170323 |
| Reference:
|
[5] Isbell J.R.: Atomless parts of spaces.Math. Scand. 31 (1972), 5-32. Zbl 0246.54028, MR 0358725 |
| Reference:
|
[6] Isbell J.R.: Private communication.April 1994. |
| Reference:
|
[7] Isbell J.R., Kříž I., Pultr A., Rosický J.: Remarks on localic groups.Springer LNM 1348, Categorial Algebra and its Applications, Proceedings, Louvain-la-Neuve, 1987, Springer-Verlag, 1988, pp.154-172. MR 0975968 |
| Reference:
|
[8] Johnstone P.T.: Stone Spaces.Cambridge University Press, Cambridge, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[9] Kříž I.: A direct description of uniform completion in locales and a characterization of LT-groups.Cahier Top. et Géom. Diff. Categ. 27 (1986), 19-34. MR 0845407 |
| Reference:
|
[10] Vickers S.: Topology via Logic.Cambridge Tracts in Theor. Comp. Sci. No. 5, Cambridge University Press, Cambridge, 1985. Zbl 0922.54002, MR 1002193 |
| . |
