A topology for a lattice-ordered group

Author:
R. H. Redfield

Journal:
Trans. Amer. Math. Soc. **187** (1974), 103-125

MSC:
Primary 06A55

DOI:
https://doi.org/10.1090/S0002-9947-1974-0327607-3

MathSciNet review:
0327607

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *G* be an arbitrary lattice-ordered group. We define a topology on *G*, called the -topology, which is a group and lattice topology for *G* and which is preserved by cardinal products. The -topology is the interval topology on totally ordered groups and is discrete if and only if *G* is a lexico-sum of lexico-extensions of the integers. We derive necessary and sufficient conditions for the -topology to be Hausdorff, and we investigate -topology convergence.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0327607-3

Keywords:
Lattice-ordered group,
topological group,
topological lattice,
-convergence,
lexico-sum,
lexico-extension,
cardinal product,
interval topology

Article copyright:
© Copyright 1974
American Mathematical Society