Order topology and interval topology of MV algebra

This paper researched the interval topology and order topology of MV algebra as well as the tightness, connectedness, completeness and the total-orderness of MV algebra. According to the properties of order convergence and the definitions of basis and sub basis, the properties of MV algebra under interval topology, order topology and correspondent operations were discussed. In addition, the paper generalized the basic properties of bold MV algebra to common MV algebra. The results show that the operations of MV algebra are continuous under either of the two topologies if and only if the elements of the operation satisfy certain requirements.