| 预拓扑分子格以及它们之间的开映射和闭映射 |
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| 引用本文： | 陈园园,路娟,李生刚. 预拓扑分子格以及它们之间的开映射和闭映射[J]. 纺织高校基础科学学报, 2005, 18(3): 229-232 |
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| 作者姓名： | 陈园园 路娟 李生刚 |
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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 |
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| 基金项目： | 国家自然科学基金;陕西师范大学校科研和教改项目 |
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| 摘 要： | 引入了预拓扑分子格的概念（它是拓扑分子格的推广）,并证明了完备格上的闭预拓扑和伪闭包算子是一一对应的.另外,定义了两个预拓扑分子格之间的连续映射、开映射、闭映射和同胚映射并证明了若干特征定理.
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| 关 键 词： | 完备格 闭预拓扑 预拓扑分子格 闭元 伪闭包算子 开映射 闭映射 |
| 文章编号： | 1006-8341（2005）03-0229-04 |
| 收稿时间： | 2005-05-18 |
| 修稿时间： | 2005-05-18 |
Pretopological molecular lattices and open mappings and closed mappings between them |
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| CHEN Yuan-yuan,LU Juan,LI Sheng-gang. Pretopological molecular lattices and open mappings and closed mappings between them[J]. Basic Sciences Journal of Textile Universities, 2005, 18(3): 229-232 |
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| Authors: | CHEN Yuan-yuan LU Juan LI Sheng-gang |
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| Abstract: | In this paper, the notion of pretopological molecular lattice is introduced, which is a generalization of topological molecular lattice. It is proved that closed pretopologies and pseudo-closure operators on a complete lattice are corresponding one by one. Moreover, the concepts of continuous mapping, open mapping, closed mapping and homeomorphic mapping are introduced and characterized. |
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| Keywords: | complete lattice closed pretopology pretopological molecular lattice closed element pseudo-closure operator open mapping closed mapping |
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