M-L-闭包系统间的特殊映射及其范畴性质

Special mappings and categorical properties of M-L-closure systems

定义了M-L-闭包系统和M-L-闭包系统间的连续映射、开映射、闭映射,讨论了这些映射的性质.证明了范畴M-L-CS(即M-L-闭包系统及它们之间的连续映射构成的范畴)是topological construct.作为应用,给出了M-L-闭包空间的积、和与商的定义.

In this paper,definitions of M-L-closure system,continuous mapping,open mapping and closed mapping of M-L-closure system are given,some properties on those mappings are discussed.It is proved that M-L-CS,the category of M-L-closure systems and continuous mappings between them,is a topological construct.As an application,it defines the notions of product M-L-closure space,sum M-L-closure space,and quotient M-L-closure space.