集合τ-标准部分的闭性  

The Closeness of the τ-standard Part of a Set

作　　者：冯晶晶[1] 

机构地区：[1]西安培华学院基础部,陕西西安710125

出　　处：《衡水学院学报》2013年第4期10-11,15,共3页Journal of Hengshui University

基　　金：陕西省教育厅专项科学研究项目(11JK0507)

摘　　要：在非标准模型下,讨论了集合标准部分的闭性.首先给出了非标准扩大模型和饱和模型这两大重要模型,以及拓扑空间中集合τ-邻域系的定义及有关命题.在此基础上给出了集合τ-单子和集合τ-标准部分的定义以及相关结论.最后证明了在非标准扩大模型和饱和模型下集合τ-标准部分是闭集的充分条件.In the nonstandard model, the standard part of a set is discussed. Two important models, nonstandard enlarged model and saturated model, are provided. It also offers the definition of neighborhood system in topological space and related topics. Based on it, the definitions and some related conclusions of monad and standard part are given. Finally, it proves that the standard part is the sufficient condition for closed set under the nonstandard enlarged model and saturated model.

关 键 词：扩大模型 饱和模型 τ-标准部分 τ-闭集 

分 类 号：O141.41[理学—数学]