连通子集性质的推广与等价刻画

Generalization and equivalent characterization of properties of connected subsets

连通子集是拓扑空间中一类特殊的子集,对其性质的研究具有重要的意义。本文推广了连通子集的两条性质,给出了其四个新的等价刻画,研究了拓扑空间中连通子集与既开又闭的子集之间的关系。另外还运用实例说明连通子集的交并非是连通子集。

Connected subsets are the special kind of subsets in topological space,and the study of their properties is of great significance.This paper generalizes two properties of connected subsets,gives four new equivalent characterizations of connected subsets,studies the relationship between connected subsets and both open and closed subsets in topological space,and provides an example showing that the intersection of connected subsets is not a connected subset.