| M-闭包空间的积、和与商 |
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| 引用本文： | 张艳霞,李生刚,鲜路.M-闭包空间的积、和与商[J].山东大学学报(理学版),2010,45(4):74-76. |
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| 作者姓名： | 张艳霞 李生刚 鲜路 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西,西安,710062 |
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| 基金项目： | 国家自然科学基金，陕西师范大学研究牛培养创新基金 |
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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。
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| 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 |
| 收稿时间： | 2009-01-17 |
Products, sums, and quotients of M-closure spaces |
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| ZHANG Yan-xia,LI Sheng-gang,XIAN Lu.Products, sums, and quotients of M-closure spaces[J].Journal of Shandong University,2010,45(4):74-76. |
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| Authors: | ZHANG Yan-xia LI Sheng-gang XIAN Lu |
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| Institution: | College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, Shaanxi, China |
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| 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. |
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| Keywords: | tolpological construct M-closure spaces topological construct product M-closure spaces sum M-closure spaces quotient M-closure spaces cartesian closed category M-weak closure operators |
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