A topology on lattice ordered groups
Author: Ivica Gusić
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.
- Nicolas Bourbaki, Éléments de mathématique, Masson, Paris, 1981 (French). Algèbre. Chapitres 4 à 7. [Algebra. Chapters 4–7]. MR 643362
- Z. Kominek and M. Kuczma, Theorems of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Arch. Math. (Basel) 52 (1989), no. 6, 595–602. MR 1007635, DOI https://doi.org/10.1007/BF01237573
- N. Bourbaki, Algèbre II, Masson, Paris, 1981.
- Z. Kominek and M. Kuczma, Theorems of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Arch. Math. 52 (1989), 595-602.
Affiliation: University of Zagreb, Faculty of Chemical Engineering and Technology, Marulićev Trg 19, p.p. 177, 10 000 Zagreb, Croatia
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