A Note on the Connectedness of the Hyperspace with Hausdorff Metric  

关于超空间连通性的一个注记(英文)

作　　者：谢琳[1] 谢朗[1] 

机构地区：[1]辽宁师范大学数学系

出　　处：《Journal of Mathematical Research and Exposition》1990年第1期32-34,共3页数学研究与评论（英文版）

摘　　要：In this note, some examples and propositions are given to answer the open question posed by E . Klein & A . C . Thompson in [ 1 ] . The main results in this note is that : if X is a metric space and there exists an arc in X, then ( 1 ) there exists an order arc a in P(X) such that α(0) is connected andis not connected ;( 2 ) there exists a point x∈X and an are β in F(X- {x}) such that and本文回答了由E.Klein与A.C.Thompson在其著作《Thery of Correspondences》中提出的一个问题。主要结果是:若X是一度量空间,且在X中存在一条弧,则在P(X)中有一条序弧α,满足条件i)α(0)是连通子集;ii) α(t)是不连通的。

关 键 词：超空间 连通性 度量空间 弧 拓扑空间 

分 类 号：O189.11[理学—数学]