| REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES |
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| 作者姓名： | XU Xiaoquan LIU Yingming |
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| 作者单位： | XU XIAOQUAN LIU YINGMING College of Mathematics，Sichuan University，Chengdu 610064，China. E-mail: xiqxu@public.nc.jx.cn
Department of Mathematics，Jiangxi Normal University，Nanchang 330027，China. College of Mathematics，Sichuan University，Chengdu 610064，China. E-mail: ymliu@scu.edu.cn |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.19831040)，the Science Foundation of the Ministry of Education of China and the Jiangxi Provincial Natural Science Foundation of China. |
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| 摘 要： | In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the Urysohn-Nachbin lemma is presented which is quite different from the classical one.
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| 关 键 词： | 定理 单调常态 法线 规则空间 正则关联 完全分配性 二进制 |
| 收稿时间： | 2/3/2020 12:00:00 AM |
| 修稿时间： | 7/3/2020 12:00:00 AM |
REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES |
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| XU Xiaoquan,LIU Yingming.REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES[J].Chinese Annals of Mathematics,Series B,2004,25(2):157-164. |
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| Authors: | XU Xiaoquan and LIU Yingming |
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| Institution: | College of Mathematics, Sichuan University, Chengdu 610064, China. Department of Mathematics, Jiangxi Normal University, Nanchang 330027, China.;College of Mathematics, Sichuan University, Chengdu 610064, China. |
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| Abstract: | In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the Urysohn-Nachbin lemma is presented which is quite different from the classical one. |
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| Keywords: | Regular relation Complete distributivity Monotone normality |
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