Topological Characterization of Consistency of Logic Theories in n-valued Lukasiewicz Logic Luk(n)

Let (F(S),p) be the n-valued logic metric space, the present paper characterizes consistency of logic theories in the propositional logic system Luk(n) by means of topological concepts in the n-valued logic metric space. It is proved that a closed theory Gamma is consistent iff it contains no interior points, iff it possesses the truth-forgotten property, iff it contains no non-empty regular sphere.