M-闭包空间的积、和与商

Products,sums,and quotients of M-closure spaces

定义了M-闭包空间以及它们之间的连续映射。证明了M-闭包空间以及它们之间的连续映射所构成的范畴M-CS是一个topological construct但不是笛卡儿闭的(其中M是任一非空指标集),在此基础上给出了乘积M-闭包空间、直和M-闭包空间以及商M-闭包空间的概念,最后指出M-闭包系统和M-弱闭包算子可以相互确定。

The notions of M-closure space and continuous mapping between two M-closure spaces are defined.It is proved that the category M-CS of all M-closure spaces and continuous mappings between them is a topological construct,but not cartesian closed （where M is any nonempty index set）.Based on this,the notions of product M-closure spaces,sum M-closure spaces,and quotient M-closure spaces are defined.Finally,it is pointed out that M-closure systems and M-weak closure operators can determine each other.