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A topology on lattice ordered groups

Author(s): Ivica Gusic
Journal: Proc. Amer. Math. Soc. 126 (1998), 2593-2597.
MSC (1991): Primary 06F30, 22A99
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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.

References:

1.
N. Bourbaki, Algèbre II, Masson, Paris, 1981. MR 84d:00002

2.
Z. Kominek and M. Kuczma, Theorems of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Arch. Math. 52 (1989), 595-602. MR 90i:46017

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Additional Information:

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

DOI: 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
Copyright of article: Copyright 1998, American Mathematical Society

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