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.
出处
《重庆理工大学学报（自然科学）》
CAS
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)
关键词
分离的
连通子集
闭集
开集
separated
connected subset
closed set
open set
