B. Banaschewski , J.J.C. Vermeulen
On the completeness of localic groups

Comment.Math.Univ.Carolinae 40,2 (1999) 293-307.

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.

Keywords: localic group, Closed Subgroup Theorem for localic groups, the uniformities of a localic group, two-sidedly complete topological groups, $LT$-groups
AMS Subject Classification: 18D35, 22A05, 54H11