In this paper, we characterize the unique determinacy, regularity, discreteness, triviality, connectivity of topological MV-algebras. Moreover, we investigate the ideal and the quotient topological MV-algebras. Especially, we prove that every topological MV-algebra is regular. As a consequence, we show that T0,T1,T2,T3 are equivalent for topological MV-algebras, ideal topological MV-algebras, and quotient topological MV-algebras. However, because MV-algebras are not rings or groups, the results are obtained that do not correspond to topological rings or topological groups.