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localic group; Closed Subgroup Theorem for localic groups; the uniformities of a localic group; two-sidedly complete topological groups; $LT$-groups
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.
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