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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A topology for a lattice-ordered group


Author: R. H. Redfield
Journal: Trans. Amer. Math. Soc. 187 (1974), 103-125
MSC: Primary 06A55
MathSciNet review: 0327607
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Abstract: Let G be an arbitrary lattice-ordered group. We define a topology on G, called the $ \mathcal{J}$-topology, which is a group and lattice topology for G and which is preserved by cardinal products. The $ \mathcal{J}$-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 $ \mathcal{J}$-topology to be Hausdorff, and we investigate $ \mathcal{J}$-topology convergence.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0327607-3
Keywords: Lattice-ordered group, topological group, topological lattice, $ \alpha $-convergence, lexico-sum, lexico-extension, cardinal product, interval topology
Article copyright: © Copyright 1974 American Mathematical Society