Affiliations: [a] College of Science, Hunan Agricultural University, Changsha, China
| [b] College of Mathematics and Finance, Xiangnan University, Chenzhou, China
Correspondence:
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Corresponding author. Jialu Zhang, College of Mathematics and Finance, Xiangnan University, Chenzhou 423000, China. Tel.: +86 18973579659; E-mail: zjl0735@163.com.
Abstract: We introduce an MV-topology on the set of all valuations of MV-algebra and then establish Lukasiewicz semantic MV-topological space. We study the topological properties of Lukasiewicz semantic MV-topology, and prove that the Lukasiewicz semantic MV-topological space is a compact zero dimension Hausdorff MV-topological space and a N-compact space. We also establish a classical topology D on the valuations set of MV-algebra, and prove that topology D is finer than the cut topology C generated by Lukasiewicz semantic MV-topology. We prove that a σ-complete lattice is an MV-algebra if and only if it is isomorphic to an MV-clopen lattice of a Stone MV-space. As an application, we use the compactness of topology D to prove the compactness of Lukasiewicz semantic and Lukasiewicz propositional logic system.
