| 拓扑系统的紧性和分离性 |
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| 引用本文： | 李高林,徐罗山.拓扑系统的紧性和分离性[J].模糊系统与数学,2007,21(2):6-13. |
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| 作者姓名： | 李高林 徐罗山 |
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| 作者单位： | 1. 扬州大学,数学科学学院,江苏,扬州,225002;盐城师范学院,数学系,江苏,盐城,224002
2. 扬州大学,数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 国家自然科学基金
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江苏省教育厅资助项目 |
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| 摘 要： | 考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。
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| 关 键 词： | 拓扑系统 紧性 分离性 locale Scott开滤子 |
| 文章编号： | 1001-7402（2007）02-0006-08 |
| 收稿时间： | 2005-12-12 |
| 修稿时间： | 2005-12-12 |
Compactness and Separation in Topological Systems |
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| LI Gao-lin,XU Luo-shan.Compactness and Separation in Topological Systems[J].Fuzzy Systems and Mathematics,2007,21(2):6-13. |
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| Authors: | LI Gao-lin XU Luo-shan |
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| Institution: | 1. Department of Mathematics,Yangzhou University, Yangzhou 225002,China; Department of Mathematics,Yancheng Teachers College,Yancheng 224002,China |
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| Abstract: | In this paper,two concepts of compactness of topological systems-spatial compactness and localic compactness are discussed.Some new characterizations of spatial compactness and relations between the two compactness are given.It is proved that spatial compactness and localic compactness are all nice generalizations of compactness for topological spaces.It is obtained that a closed subsystem,a finite topological sum,or a topological product of compact topological system(s) is still a compact topological system.It is also proved that a compact(strong) T2 topological system is a(strong) T4 topological system.A characterization of strong T2 topological system by convergence of ideals is also given. |
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| Keywords: | Topological System Compactness (Strong) T2 Separation Locale Net Filter |
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