J4 ›› 2010, Vol. 45 ›› Issue (4): 74-76.
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ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu
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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.
Key words: M-closure spaces; topological construct; product M-closure spaces; sum M-closure spaces; quotient M-closure spaces; cartesian closed category; M-weak closure operators
ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu. Products, sums, and quotients of M-closure spaces[J].J4, 2010, 45(4): 74-76.
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