| Locale范畴中的零维性 |
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| 引用本文： | 贺伟,罗懋康.Locale范畴中的零维性[J].数学学报,1998,41(3):539-544. |
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| 作者姓名： | 贺伟 罗懋康 |
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| 作者单位： | 陕西师范大学数学系(贺伟)，四川联合大学数学系(罗懋康) |
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| 基金项目： | 国家自然科学基金,国家教委博士点基金 |
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| 摘 要： | 本文讨论ｌｏｃａｌｅ的零维性质，主要结果有：（１）给出ｌｏｃａｌｅＡ的核映射（ｎｕｃｌｅｕｓ）构成的ｌｏｃａｌｅＮ（Ａ）中上确界的点式刻划，并得到了Ｎ（Ａ）的紧性与Ａ的紧性之间的关系；（２）给出零维ｌｏｃａｌｅ与ｃｏｈｅｒｅｎｔｌｏｃａｌｅ之间的关系，以及零维ｌｏｃａｌｅ的紧零维反射；（３）给出零维ｌｏｃａｌｅ范畴在ｌｏｃａｌｅ范畴中的刻划．
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| 关 键 词： | Locale范畴，零维locale |
| 收稿时间： | 1995-3-13 |
Zero dimensionality in the Category of Locales |
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| He Wei.Zero dimensionality in the Category of Locales[J].Acta Mathematica Sinica,1998,41(3):539-544. |
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| Authors: | He Wei |
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| Institution: | He Wei (Department of Mathematics, Shanxi Teachers University, Xi′an 710062, China) Luo Maokang (Department of Mathematics, Sichuan Union University, Chengdu 610064, China) |
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| Abstract: | In this paper, we investigate the zero dimensional property for locales, the main results are following: (1) The pointwise characterization of joins of nuclei in a locale is given, the relationship between compactness of a locale A and compactness of N(A) is obtained.(2) The compact zero dimensional refletion of a zero dimensional localeis obtained in much simple form. (3) The category theory characterization of the category of zero dimensional locales is obtained. |
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| Keywords: | Category of locales Zero dimensional locale |
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