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| REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES |
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Citation： |
XU Xiaoquan,LIU Yingming.REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES[J].Chinese Annals of Mathematics B,2004,25(2):157~164 |
| Page view： 1137
Net amount： 768 |
Authors： |
XU Xiaoquan; LIU Yingming |
Foundation： |
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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| 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. |
Keywords： |
Regular relation, Complete distributivity, Monotone normality |
Classification： |
03E20, 06D10, 54D15, 54F05 |
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