基-序列中紧空间的若干性质  

Some Properties of Base-sequentially Mesocompact Spaces

作　　者：王荣欣[1] 王尚志[2] 牟磊[2] 

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]首都师范大学数学科学学院,北京100037

出　　处：《四川师范大学学报（自然科学版）》2012年第5期599-604,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10901045;11201112);河北省自然科学基金(A2010000828)资助项目

摘　　要：推广文献(Top Appl,2003,128(2/3):145-156.)引入的基-仿紧空间的概念,引入基序列中紧空间:空间X称为基-序列中紧空间,如果X有一个基B,满足|B|=w(X),且对X的任意开覆盖U,都存在B'■B,B'是U的收敛序列有限的开加细.它是基-仿紧性和序列中紧性的推广.通过构造空间X的基的收敛序列有限的开加细,主要研究了基-序列中紧空间的性质,证明了:1)基-序列中紧空间与其他基覆盖性质间的蕴含关系;2)在完备映射下基-序列中紧性是逆保持的;3)基-序列中紧空间的乘积性质等.所得结果不仅推广了基-仿紧空间的性质,在理论上也完善了拓扑空间的基-覆盖性质.Generalizing paracompactness given by J. E. Porter（ Top Appl,2003,128 （2/3）：145 -156. ）, we introduce a new concept, base-sequencially mesocompactness. A space X is called base-sequencially mesoeompact if there is a base B of X with I B I = w（X） , such that for every open cover U for X, there is a subfamily B＇ _B which is an open convergent sequence-finite refinement of U. The notion of base-sequentially mesocompaetness is a generalization of base-paracompactness and sequentially mesocompactness. By constructing convergent sequence-finite refinement of base, we mainly study the properties of base-sequentially mesocompact spaces. We discuss the followings：l ） the implication relation between base-sequentially mesocompaetness and other base covering properties, 2） the inverse-preserving property of base-sequentially mesocompactness under perfect map, and 3 ） the product properties of base-se- quentially mesoeompactness. The results generalize properties of base-paracompacness and bring the base-cover properties of topological spaces to completion.

关 键 词：基-序列中紧 基-正规 完备映射 乘积 

分 类 号：O189.1[理学—数学]