MV代数的序拓扑和区间拓扑

Order Topology and Interval Topology of MV Algebra

研究了MV代数的区间拓扑和序拓扑及MV代数下的拓扑紧性、连结性、完备性和全序性.通过序收敛的性质和基与子基的概念分别探讨了MV代数及其运算在序拓扑和区间拓扑下的性质,并且把标准MV代数的基本性质推广到了一般意义下的MV代数.研究表明,MV代数中的运算在这两种拓扑下连续,当且仅当进行运算的元之间满足一定条件.

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.