Filter topologies on MV-algebras
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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.
KeywordsMV-algebra Filter topology Hausdorff space Semisimple Dense
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The authors declare that they have no conflict of interest.