| Domain函数空间上Isbell拓扑与Scott拓扑何时相同 |
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| 引用本文： | 奚小勇.Domain函数空间上Isbell拓扑与Scott拓扑何时相同[J].数学学报,2005,48(5):1021-102. |
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| 作者姓名： | 奚小勇 |
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| 作者单位： | [1]四川大学数学学院,成都610064 [2]徐州师范大学数学系,徐州221009 |
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| 基金项目： | 国家自然科学基金资助项目;教育部博士点基金资助项目 |
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| 摘 要： | 本文证明了,若L是一个双完备的连续DCPO,则对所有的RW-空间X,函数空间X→L]上的Isbell拓扑和Scott拓扑相同当且仅当L是有最小元的L-Domain.而且还证明了,若X是核紧的局部连通空间,则对所有有最小元的连续L-DomainL,X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.特别地,若X是连续DCPO,则对所有有最小元的连续L-DomainL,函数空间X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.这也给出由Lawson和Mislove提出的一个公开问题的一个部分回答.
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| 关 键 词： | 核紧空间 RW-空间 连续L-Domain |
| 文章编号： | 0583-1431（2005）05-1021-08 |
| 收稿时间： | 2004-02-25 |
| 修稿时间： | 2004-02-252004-12-30 |
When Do the Isbell and Scott Topologies Agree on Domain Function Spaces |
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| Xi XiaoYong.When Do the Isbell and Scott Topologies Agree on Domain Function Spaces[J].Acta Mathematica Sinica,2005,48(5):1021-102. |
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| Authors: | Xi XiaoYong |
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| Institution: | Xiao Yong XI Mathematics College of the Sichuan University, Chengdu 610064, P. R. China Mathematics College of Xuzhou Normal University, Xuzhou 221009, P. R. China |
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| Abstract: | It is proved in this paper that if L is a bicomplete continuous DCPO, then the Isbell and Scott topologies agree on function spaces X →L] for all RW-spaces X iff L is an L-Domain with a least element. Moreover, it is obtained that, if X is a core compact and locally connected space, then the Isbell and Scott topologies agree on functions space X →L] for all continuous L-Domain L with a least element if and only if X is an RW-space. Particularly, if X is a continuous DCPO, then the Isbell and Scott topologies agree on function spaces X →L] for all continuous L-Domain L with a least element iff X is an RW-space. This also gives a partial solution to the open problem presented by Lawson and Mislove. |
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| Keywords: | Core compact spaces RW-spaces Continuous L-Domain |
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