On (para, quasi) topological MV-algebras

Abstract In this paper, the notions of (para, quasi, semi) topological MV-algebras are defined and their related properties are studied. Also, topologies with which an MV-algebra can be a (para, semi) topological MV-algebra are obtained. Clearly, a topological MV-algebra is a (para, quasi, semi) topological MV-algebra, but the converse is not true, as shown by an example. In addition, we study ideals and filters in (para, quasi) topological MV-algebras, and we show that a quasitopological MV-algebra is a topological MV-algebra if the ideal {0}, or equivalently, the filter {1} is open.