Abstract
Let A be a lattice-ordered group. Gusić showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusić’s theorem, and reveal the very nature of a “C-group” of Gusić in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.
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This work was supported by the Fund of Elitist Development of Beijing (Grant No. 20071D1600600412) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
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Yang, Y. The C-topology on lattice-ordered groups. Sci. China Ser. A-Math. 52, 2397–2403 (2009). https://doi.org/10.1007/s11425-009-0098-3
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DOI: https://doi.org/10.1007/s11425-009-0098-3