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 s-complete lattice is an MV-algebra if and only if ...
