| 关于Scott拓扑存在开滤子拓扑基的分配备格 |
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| 引用本文： | 谢琳,宋玉靖.关于Scott拓扑存在开滤子拓扑基的分配备格[J].数学学报,2000,43(2):213-220. |
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| 作者姓名： | 谢琳 宋玉靖 |
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| 作者单位： | 辽宁师范大学数学系辽宁大连 116029 |
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| 基金项目： | 辽宁省自然科学基金资助 |
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| 摘 要： | 本文利用引入的ＫＳ性质，刻划了那些其Ｓｃｏｔｔ拓扑可由开滤子生成的分配备格，该结果也是对［１］中一公开问题的一种解答．本文的刻划定理对于判定分配备格的Ｓｃｏｔｔ拓扑是否与Ｓｃｏｔｔ开滤子拓扑一致具有较强的可操作性，应用该刻划定理给出大量非连续格，其Ｓｃｏｔｔ拓扑具有开滤子基．
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| 关 键 词： | Scott拓扑 Scott开滤子 frame 空间式frame |
| 文章编号： | 0583-1431(2000)02-0213-08 |
| 修稿时间： | 1997年5月4日 |
On Distributive Complete Lattices for Which the Scott Topology Has a Basis of Open Filters |
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| XIE Lin,SONG Yu-jing.On Distributive Complete Lattices for Which the Scott Topology Has a Basis of Open Filters[J].Acta Mathematica Sinica,2000,43(2):213-220. |
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| Authors: | XIE Lin SONG Yu-jing |
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| Institution: | XIE Lin; SONG Yu-jing (Department of Mathematics , Lioaning Normal University, Dalian 116029, P. R. China) |
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| Abstract: | In this paper, AS property is introduced, and a problem in 1] is discussed. First, the paper shows that the Scott topology on a distributive complete lattice L has a basis of open filters if and only if L is a KS. frame for some ordinal number a, i.e., KS frame. By the result, one can judge whether the Scott topology and the Scott open filter topology on a distributive complete lattice are coincide. Then some KS frames are constructed in the paper, which are not continuous. |
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| Keywords: | The Scott topology The Scott open filter Frame Spatial frame |
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