J4 ›› 2010, Vol. 45 ›› Issue (4): 74-76.
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张艳霞，李生刚*，鲜路
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基金资助:
国家自然科学基金资助项目(10871121)；陕西师范大学研究生培养创新基金资助项目(2009CXS029)
ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu
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摘要：
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。
关键词: M-闭包空间;topological construct; 乘积M-闭包空间;直和M-闭包空间;商M-闭包空间;笛卡儿闭范畴; M-弱闭包算子
Abstract:
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
张艳霞，李生刚*，鲜路. M-闭包空间的积、和与商[J]. J4, 2010, 45(4): 74-76.
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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http://lxbwk.njournal.sdu.edu.cn/CN/Y2010/V45/I4/74
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