Geodesic
On the completeness of localic groups
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 293-307.

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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.
Classification : 18D35, 22A05, 54E15, 54H11
Keywords: localic group; Closed Subgroup Theorem for localic groups; the uniformities of a localic group; two-sidedly complete topological groups; $LT$-groups 
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Banaschewski, B.; Vermeulen, J. J. C. On the completeness of localic groups. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 293-307. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a10/