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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A topology on lattice ordered groups
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by Ivica Gusić PDF
Proc. Amer. Math. Soc. 126 (1998), 2593-2597 Request permission

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
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Additional Information
  • Ivica Gusić
  • 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
  • Received by editor(s): February 28, 1996
  • Received by editor(s) in revised form: February 13, 1997
  • Communicated by: Roe Goodman
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2593-2597
  • MSC (1991): Primary 06F30, 22A99
  • DOI: https://doi.org/10.1090/S0002-9939-98-04386-X
  • MathSciNet review: 1452805