关于弱J-空间的一些性质  

Some properties about the weak J-space

作　　者：汪贤华[1] 王延庚[2] 

机构地区：[1]北京石油化工学院数理部,北京102617 [2]西北大学数学系,陕西西安710069

出　　处：《西北大学学报（自然科学版）》2004年第4期383-385,共3页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学基金资助项目(98SL06)

摘　　要：目的　研究弱J 空间、半弱J 空间及其乘积空间和J 空间的锥空间的一些性质。方法　在前人研究J 空间的基础之上,用类比的思想以及构造新空间(乘积空间与商空间)的方法来研究与弱J 空间有关的一些性质。结果　得到了有关弱J 空间和半弱J 空间的一些等价命题及乘积性质,也得到了J 空间的锥空间的性质。结论　①设{X1,X2,K}是空间X的闭覆盖并且满足K紧,X1∩X2= ,则X是弱J 空间当且仅当X1和X2是弱J 空间,且X1或X2紧;②判断乘积空间X1×X2是弱J 空间的一些充分必要条件;③如果X是连通的J 空间,那么Δ(X)是半弱J 空间。Aim To discuss the properties of the weak J-space and the semi-weak J-space, and also to investigate some properties about the Cartesian products and the cone of the J-space.Methods Based on the study of J-space by E.Michael, the method for comparing and constructing new spaces (the Cartesian products and the quotient spaces) are adopted to study some properties about the weak J-space.Results Obtained some equivalent propositions of the weak J-space and the semi-weak J-space, and also some properties about the Cartesian products. Moreover, the properties about the cone of the J-space are also been discussed.Conclusion ① Let{X_1,X_2,K} be closed cover of X with K compact and X_1∩X_2=,then X is a weak J-space if and only if X_1 and X_2 are weak J-spaces, and X_1 or X_2 is compact.② The necessary and sufficient conditions of deciding the Cartesian products of X_1 and X_2 to be weak J-spaces.③ If X is connected J-space, then the cone of the space X, that is Δ(X), is a semi-weak J-space.

关 键 词：拓扑空间 强J-空间 J-空间 弱J-空间 单调映射 锥空间 

分 类 号：O189.1[理学—数学]