紧性的非标准定义及其性质  

The compactness defined by nonstandard analysis methods and its properties

作　　者：翟美娟[1] 马春晖[1] 史艳维[2] 麦安婵 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]西安培华学院基础部,陕西西安710125 [3]西安陆军学院科学文化基础教研室,陕西西安710108

出　　处：《纺织高校基础科学学报》2009年第3期276-278,共3页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金(2007A12);西安建筑科技大学青年科技基金资助项目(QN833)

摘　　要：在非标准扩大模型和拓扑的非标准定义基础之上,对拓扑空间中紧性的概念及相关结论进行了描述和刻画.一方面,这种新的定义与一般的紧性定义是一致的;另一方面,这种新的定义方法简化了原有的概念和结论,使它们的本质特性更为清晰,因而在一定程度上发展了拓扑空间中原有的紧性理论.Based on the nonstandard topology definition and enlarged model, the concept of compactness in the topological space are described and characterized in this paper. This new definition of compactness is identical to the general one. On the other hand, this new definition method simplify many concepts and conclusions in the topological space and clarify their nature character. Therefore, the compactness theory of the topological space is improved to a certain degree.

关 键 词：拓扑 单子 转换原理 紧性 

分 类 号：O141.41[理学—数学]