关于可数中紧空间的映射定理  

Mapping Theorems on Countably Mesocompact Spaces

作　　者：王秋利[1] 燕鹏飞[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2012年第2期5-7,共3页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10971125)

摘　　要：通过可数中紧空间的等价刻画给出了关于可数中紧性的几个映射定理:1)可数中紧性在闭的紧覆盖映射下是保持的;2)可数中紧的Frechet空间在闭映射下的像是可数中紧的;3)可数中紧性的拟完全原象是可数中紧的;4)可数中紧空间与紧空间的积空间是可数中紧的.Several ma characterizations： pping theorems on countably mesocompact spaces are given through equivalent Countably mesocompactness is preserved under closed and compact-covering mappings; 2） The image of a countably mesocompact and Frechet space under a closed mapping is countahly mesocompact; 3） The original image of a countably mesocompact space under a quasi-perfect mappings is countably mesocompact; 4） If X is a countably mesocompact space and Y is a compact space, then X×Y is also a countably mesocompact space.

关 键 词：可数中紧空间 紧覆盖映射 闭映射 拟完全映射 

分 类 号：O189.11[理学—数学]