| R0代数上的一致拓扑空间 |
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| 引用本文： | 罗清君. R0代数上的一致拓扑空间[J]. 山东大学学报(理学版), 2013, 48(2): 72-78 |
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| 作者姓名： | 罗清君 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062;西安财经学院统计学院,陕西西安710100 |
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| 基金项目： | 国家自然科学基金资助项目，陕西省教育厅自然科学基金资助项目 |
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| 摘 要： | 利用MP滤子F在R0代数M上诱导一致拓扑JF,得出了(M,JF)是不连通的、零维的、局部紧的、完全正则的第一可数空间, (M,JF)是T0空间当且仅当F=｛1｝。 证明了R0代数M中的运算′, ∨与→在(M,JF)中均连续。 最后, 讨论了商代数中一致拓扑的性质。
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| 关 键 词： | R0代数 MP滤子 一致拓扑 |
| 收稿时间： | 2012-08-15 |
Uniform topological spaces on R0 algebras |
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| Affiliation: | 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;2. College of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, Shaanxi, China |
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| Abstract: | It is proved that the uniform topological space induced by a filter in an R0 algebra is a disconnected, zero-dimensional, locally compact, completely regular and first countable space, and a T0 space if and only if the filter is equal to ｛1｝. Also, we proved that the negative operation, the join operation and the implication operation are continuous in the uniform topological space. Finally, some properties of the uniform topology are discussed on the quotient R0 algebra under the equivalence relation induced by a filter. |
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| Keywords: | R0 algebra filter MP uniform topology |
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