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Cantor extension of a half lattice ordered group. (English) Zbl 0938.06014
Half lattice ordered groups have been studied by M. Giraudet and F. Lucas [Fundam. Math. 139, No. 2, 75-89 (1991; Zbl 0766.06014)]. Let $$G$$ be a half lattice ordered group; then there are subsets $$G{\uparrow}$$ and $$G{\downarrow}$$ of $$G$$ such that $$G{\uparrow}\cup G{\downarrow}=G$$ and $$G{\uparrow}\cap G{\downarrow}=\emptyset$$. Moreover, $$G{\uparrow}$$ is a lattice ordered group (under the operations induced from $$G$$). The author deals with the case when the group operation in $$G{\uparrow}$$ is abelian. The Cantor extension $$G'$$ of $$G$$ is defined by the requirements that a) $$G'$$ is $$o$$-complete; b) $$G$$ is an hl-subgroup of $$G'$$; c) every element of $$G'$$ is an $$o$$-limit in $$G'$$ of a fundamental sequence in $$G$$. It is proved that the Cantor extension of $$G$$ exists and that it is uniquely determined up to isomorphism leaving all the elements of $$G$$ fixed.

##### MSC:
 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 06F15 Ordered groups
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##### References:
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