Abstract
We show that every MV-algebra A can be naturally equipped with a filter topology such that A is a topological MV-algebra, which improves the main results on C-topological lattice-ordered groups in both Yang (Sci China Ser A 52(11):2397–2403, 2009) and Gusić (Proc Am Math Soc 126(9):2593–2597, 1998). Furthermore, for a 2-divisible MV-algebra A, we show that the filter topological space is Hausdorff if and only if A is semisimple.
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References
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Yang Y (2009) The C-topology on lattice-ordered groups. Sci China Ser A 52(11):2397–2403
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Communicated by Y. Yang.
The authors acknowledge the support of NSFC, Grant 11271040.
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Luan, C., Yang, Y. Filter topologies on MV-algebras. Soft Comput 21, 2531–2535 (2017). https://doi.org/10.1007/s00500-017-2574-y
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DOI: https://doi.org/10.1007/s00500-017-2574-y