# On the completeness of localic groups

Bernhard Banaschewski; Jacob J. C Vermeulen

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 2, page 293-307
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topBanaschewski, Bernhard, and Vermeulen, Jacob J. C. "On the completeness of localic groups." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 293-307. <http://eudml.org/doc/248420>.

@article{Banaschewski1999,

abstract = {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.},

author = {Banaschewski, Bernhard, Vermeulen, Jacob J. C},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {localic group; Closed Subgroup Theorem for localic groups; the uniformities of a localic group; two-sidedly complete topological groups; $LT$-groups; localic group; closed subgroup theorem for localic groups; uniformities of localic group; two-sidedly complete topological groups; -groups; frame homomorphisms},

language = {eng},

number = {2},

pages = {293-307},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On the completeness of localic groups},

url = {http://eudml.org/doc/248420},

volume = {40},

year = {1999},

}

TY - JOUR

AU - Banaschewski, Bernhard

AU - Vermeulen, Jacob J. C

TI - On the completeness of localic groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1999

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 40

IS - 2

SP - 293

EP - 307

AB - 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.

LA - eng

KW - localic group; Closed Subgroup Theorem for localic groups; the uniformities of a localic group; two-sidedly complete topological groups; $LT$-groups; localic group; closed subgroup theorem for localic groups; uniformities of localic group; two-sidedly complete topological groups; -groups; frame homomorphisms

UR - http://eudml.org/doc/248420

ER -

## References

top- Banaschewski B., Completion in Pointfree Topology, Lecture Notes in Mathematics and Applied Mathematics No. 2/96, University of Cape Town, 1996. Zbl1034.06008
- Banaschewski B., Hong S.S., Pultr A., On the completion of nearness frames, Quaest. Math. 21 (1998), 19-37. (1998) Zbl0931.54025MR1658467
- Bourbaki N., General Topology, Herrman, Paris and Addison-Wesley, Reading, Massachusetts, 1966. Zbl1107.54001
- Isbell J.R., Uniform spaces, A.M.S. Mathematical Survey 12, Providence, Rhode Island, 1964. Zbl0124.15601MR0170323
- Isbell J.R., Atomless parts of spaces, Math. Scand. 31 (1972), 5-32. (1972) Zbl0246.54028MR0358725
- Isbell J.R., Private communication, April 1994.
- 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. MR0975968
- Johnstone P.T., Stone Spaces, Cambridge University Press, Cambridge, 1982. Zbl0586.54001MR0698074
- 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. (1986) MR0845407
- Vickers S., Topology via Logic, Cambridge Tracts in Theor. Comp. Sci. No. 5, Cambridge University Press, Cambridge, 1985. Zbl0922.54002MR1002193

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.