| 关于CSS空间及相关结论 |
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| 引用本文： | 彭良雪,王丽霞.关于CSS空间及相关结论[J].数学物理学报(A辑),2010,30(2):358-363. |
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| 作者姓名： | 彭良雪 王丽霞 |
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| 作者单位： | 北京工业大学应用数理学院,北京,100124 |
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| 基金项目： | 北京市教育委员会科技发展计划面上项目，教育部留学回国人员科研启动基金 |
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| 摘 要： | CSS空间是指空间中的紧集都是一致G_δ集的空间.该文的第一部分,主要证明了具有拟G_δ(2)对角线的空间是CSS空间.另外,还证明了如果X是可数个闭的CSS空间的并,则X是CSS空间.CSS空间的可数积空间是CSS空间;第二部分证明了如果空间X可以表示成可数个闭的β空间(或半层空间)的并,则X是β空间(或半层空间).
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| 关 键 词： | CSS空间 拟Gδ(2) 对角线 g 函数 β空间 |
| 收稿时间： | 2008-10-15 |
| 修稿时间： | 2009-09-15 |
On CSS Spaces and Related Conclusions |
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| PENG Liang-Xue,WANG Li-Xia.On CSS Spaces and Related Conclusions[J].Acta Mathematica Scientia,2010,30(2):358-363. |
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| Authors: | PENG Liang-Xue WANG Li-Xia |
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| Institution: | College of Applied Science, Beijing University of Technology, Beijing 100124 |
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| Abstract: | A space X is a CSS space if compact sets are uniformly Gδ sets. In the first part of this note, the authors mainly prove that, if a space X has a quasi-Gδ (2) diagonal, then X is a CSS space. They also show that the countable product of CSS spaces is a CSS space, and if $X$ is the union of a family of countable closed CSS subspaces, then X is a CSS space. In the second part, the authors mainly show that, if X is the union of a family of countable closed β-subspaces (semi-stratifiable spaces), then X is a β-space (semi-stratifiable space). |
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| Keywords: | CSS space g function |
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