模糊拓扑空间中有限覆盖性质的非标准刻画  

The nonstandard characterization of finite covering property in fuzzy topological spaces

作　　者：史艳维[1] 马春晖[2] 

机构地区：[1]西安培华学院基础部,陕西西安710125 [2]西安建筑科技大学理学院,陕西西安710055

出　　处：《纺织高校基础科学学报》2012年第3期324-326,共3页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金(2007A12);陕西省教育厅专项科学研究项目(11JK0507)

摘　　要：在非标准扩大模型下,讨论了模糊拓扑空间中有限覆盖性质的非标准刻画.将模糊集合扩张为非标准模糊集合,并定义了模糊点的单子.借助模糊点的单子给出了有限覆盖性质的非标准刻画,并在此基础上得到了有限覆盖空间的非标准刻画.证明了有限覆盖空间的Tychonoff乘积定理.In nonstandard enlarged model,the nonstandard characterization of finite covering property is discussed in fuzzy topological spaces.Firstly,fuzzy sets are extended to nonstandard fuzzy sets,and the monad of fuzzy point is defined.Then,the nonstandard characterization of finite covering property is obtained by the monad,and the finite covering spaces are nonstandard characterized.Finally,Tychonoffproducts theorem of finite covering spacess is proved by these nonstandard characterizations.

关 键 词：非标准扩大模型 单子 有限覆盖性质 Tychonoff乘积定理 

分 类 号：O141.41[理学—数学]