| 仿sober与超sober拓扑空间 |
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| 引用本文： | 袁珍艳,徐罗山.仿sober与超sober拓扑空间[J].扬州大学学报(自然科学版),2008,11(4). |
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| 作者姓名： | 袁珍艳 徐罗山 |
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| 作者单位： | 1. 宿迁高等师范学校,数学系,江苏,宿迁,223800;扬州大学,数学科学学院,江苏,扬州,225002
2. 扬州大学,数学科学学院,江苏,扬州,225002 |
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| 摘 要： | 对拓扑空间的sober分离性细致分析后引入类似于sober性的另外两种分离性：仿sober和超sober分离性;讨论了诸分离性的相关性质和相互关系,证明了非T1的仿sober空间一定是连通的、可分的sober空间;还探讨了domain上Scott拓扑与仿sober、超sober分离性的关系,证明了仿（超）sober偏序集均为代数domain.
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| 关 键 词： | 仿sober拓扑 超sober拓扑 特殊化序 domain Scott拓扑 |
On pseudo-sober topological spaces and ultra-sober topological spaces |
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| YUAN Zhen-yan,XU Luo-shan.On pseudo-sober topological spaces and ultra-sober topological spaces[J].Journal of Yangzhou University(Natural Science Edition),2008,11(4). |
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| Authors: | YUAN Zhen-yan XU Luo-shan |
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| Institution: | YUAN Zhen-yan1,2,XU Luo-shan2(1.Dept of Math,Suqian Teachers Sch,Suqian 223800,China,2.Sch of Math Sci,Yangzhou Univ,Yangzhou 225002,China) |
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| Abstract: | Soberity is a separation property of topological spaces.In this paper,two concepts of sober-like separations: pseudo-sober separation and ultrasober separation are introduced and investigated.Some properties and relations of them are drawn.It is proved that a non-T1 pseudo-sober topological space must be sober,separable and connected.The relationships of domains in the Scott topology and pseudo-(ultra-) sober spaces are also explored.It is proved that a pseudo-(ultra-) sober poset is an algebraic domain. |
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| Keywords: | domain |
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