The Distance Space And Continuous Mapping Of MV - Algebra

MV-algebra is an important theoretical foundation of the study of logic alge-bras. The definition of a distance function in MV-algebra is given, and its properties are discussed in this paper. Secondly, the " (?) " operation is introduced in the MV-algebra, then the distance function defined on MV-algebra is studied deeply. And on this basis, the definition of the open set and continuous mapping in general met-ric space are introduced into the distance space of MV-algebra. Finally, a pseudo distance function of MV-algebra is defined by MV-homomorphism, and the inter-nal relation between pseudo lattice valued distance and lattice valued distance is revealed.The construction of chapters and the concrete contents of this paper are as follows:Chapter 1:Preliminaries. We give the basic concepts of lattice, residuate lat-tice, MV-algebra, and the lattice valued distance in MV-algebra which will be used in this paper.Chapter 2:A kind of distance function and its equivalent representation of MV-algebra. At first, a form of distance function in MV-algebra is given, and the basic properties of it are discussed; Then, the "(?)" operation is introduced in the MV-algebra, the equivalent representation of the distance function in MV-algebra is derived. Thus, the distance function defined on MV-algebra is studied deeply.Chapter 3:The spherical neighborhood and open set in the distance space of MV-algebra. The definition of the open set and continuous mapping in general metric space are introduced into the distance space of MV-algebra. And some good properties are obtained.Chapter 4:The continuous mapping between the distance space of MV-algebra. Firstly, the concept of the continuous mapping among the distance space of MV-algebra is introduced. Secondly, it is proved that the distance function is automatic continuous and the operation on MV-algebra is continuous. Thirdly, the relationship between MV-isomorphism and the continuous mapping is studied.Chapter 5:A pseudo distance function of MV-algebra. In this chapter, a pseudo distance function of MV-algebra is defined, and its related properties are discussed. Then, the internal relation between pseudo lattice valued distance and lattice valued...