A topology for a lattice-ordered group
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- by R. H. Redfield PDF
- Trans. Amer. Math. Soc. 187 (1974), 103-125 Request permission
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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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