Fell-拓扑的伪紧性(英文)  

Pseudocompactness of the Fell Topology

作　　者：侯吉成[1] 

机构地区：[1]四川大学数学学院

出　　处：《数学进展》2002年第3期271-274,共4页Advances in Mathematics（China）

基　　金：Supported partly by Scientic Research Foundation for Returned Overseas Chineses Scholars of the State EducationMinistry of China.

摘　　要：设X是拓扑空间.CL(X)表示X的所有非空闭子集的族.本文得到了下述结果:在CL(X)上的Fell-拓扑是伪紧的当且仅当X是feebly-紧或者非局部紧或者非σ-紧.由此得到了对于伪紧性不是闭遗传的两类新的拓扑空间.Let X be a topological space and CL(X) the hyperspace of all closed nonempty subsets of X. We prove that for a regular space X, the Fell topology on CL(X) is pseudocompact if and only if X satisfies one of the conditions: (i) X is feebly compact, (ii) X is not σ-compact, (iii) X is not locally compact. As a consequence, we find two new classes of topological spaces which are not closed-hereditary for pseudocompactness.

关 键 词：超空间 Fell-拓扑 伪紧 局部紧 σ-紧 拓扑空间 

分 类 号：O177.4[理学—数学]