| 拟连续Domain的若干拓扑性质 |
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| 引用本文： | 杨金波,罗懋康.拟连续Domain的若干拓扑性质[J].模糊系统与数学,2006,20(3):69-76. |
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| 作者姓名： | 杨金波 罗懋康 |
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| 作者单位： | 四川大学,数学学院,四川,成都,610064;江西师范大学,数学系,江西,南昌,330027;四川大学,长江数学中心,四川,成都,610064 |
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| 基金项目： | NSFC(10331010)，theNationalScienceFundforDistinguishedYoungScholarsandTheResearchFundfortheDoctoralProgramofHigherEducation |
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| 摘 要： | 对拟连续Domain D证明了:(1)双拓扑空间(D,σ(D),(D))为两两完全正则空间;(2)若D有可数基,则(max(D),σ(D)max(D))为正则空间当且仅当它为Polish空间;(3)拓扑空间(D,σb(D))为零维Tychonoff空间,其中σb(D)为D上Scott拓扑的b-拓扑。
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| 关 键 词： | 拟连续Domain 两两完全正则 极大点 Polish空间 b-拓扑 |
| 文章编号： | 1001-7402（2006）03-0069-08 |
| 收稿时间： | 2005-09-03 |
| 修稿时间： | 2005年9月3日 |
Some Topological Properties of Quasicontinuous Domains |
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| YANG Jin-bo,LUO Mao-kang.Some Topological Properties of Quasicontinuous Domains[J].Fuzzy Systems and Mathematics,2006,20(3):69-76. |
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| Authors: | YANG Jin-bo LUO Mao-kang |
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| Institution: | 1. Institute of Mathematics, Sichuan University, Chengdu 610064,China; 2. Department of Mathematics,Jinagxi Normal University, Nanchang 330027,China; 3. Yangtze Center of Mathematics,Sichuan University,Chengdu 610064,China |
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| Abstract: | For a quasicontinuous domain D, we prove that (1) the bitopology space (D,σ(D),ω(D)) is pairwise completely regular, (2) for an ω-quasicontinuous domain D, the maximal points max(D) in its Scott topology inherited from D is regular if and only if it is a Polish space, and (3) the space (D,σb(D)) is zero-dimensional Tychonoff, where σb(D) is the b-topology for the Scott topology on D. |
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| Keywords: | Quasicontinuous Domain Pairwise Completely Regular Maximal Point Polish Space b-topology |
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