连通子集的充要条件  

The Necessary and Sufficient Condition for Connected Subset

作　　者：韩婵[1] 陈东立[2] 

机构地区：[1]西安建筑科技大学华清学院,西安710043 [2]西安建筑科技大学,西安710055

出　　处：《重庆理工大学学报（自然科学）》2013年第12期137-138,共2页Journal of Chongqing University of Technology：Natural Science

基　　金：陕西省教育厅专项科学研究项目(11JK0507);西安建筑科技大学青年科技基金(QN1135)

摘　　要：研究了连通子集的2个充分必要条件,即Y是拓扑空间X的一个连通子集当且仅当Y不是X中2个非空分离子集的并,及在Y中既开又闭的子集只有Y与。在此基础上,证明了包含多于一点的离散空间是不连通空间。In this paper, two of the necessary and sufficient conditions for connected subset are stud- ied. That is a subset Y of topological space X is connected if is not the union of two non-void separated subsets of X , and the only subset of which are both open and closed in Yare Yand the void set. Based on this, it is proved that a discrete space containing more than one point is not connected.

关 键 词：分离的 连通子集 闭集 开集 

分 类 号：O189.11[理学—数学]