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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A topology on lattice ordered groups


Author: Ivica Gusic
Journal: Proc. Amer. Math. Soc. 126 (1998), 2593-2597
MSC (1991): Primary 06F30, 22A99
MathSciNet review: 1452805
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Abstract: We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set $C$ of admissible elements ($C$-topology). If a lattice ordered group is 2-divisible and satisfies a version of Archimedes' axiom ($C$-group), then we show that the $C$-topology is Hausdorff. Moreover, we show that a $C$-group with the $C$-topology is a topological group.


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Ivica Gusic
Affiliation: University of Zagreb, Faculty of Chemical Engineering and Technology, Marulićev Trg 19, p.p. 177, 10 000 Zagreb, Croatia
Email: igusic@pierre.fkit.hr

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04386-X
PII: S 0002-9939(98)04386-X
Keywords: Lattice ordered group, set of admissible elements, $C$-topology, $C$-group
Received by editor(s): February 28, 1996
Received by editor(s) in revised form: February 13, 1997
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society