关联子集与不连通空间的等价刻画

Correlative Subsets and Equivalent Characterization of Disconnected Spaces

通过对点集拓扑学中基本概念及相互关系的研究,引入内导集的概念,再以内导集概念为基础引入关联子集的概念,并对其基本性质及与其他概念的关系进行了初步探讨,取得了一些较好的结果.利用关联型不连通空间与不连通空间的性质及其相互关系给出了不连通空间的几个等价刻画.

By means of the deep researches on basic concepts of point set topology and relationships among them, and the thought and method of dual category the concept of internal derived set was introduced in point set topology. Based on the concept of internal derived set, the concept of correlative subset was proposed, and its fundamental properties and relationships between it and other concepts were studied, and some good results were obtained. At last, as the application of internal derived set and correlative subset, several equivalent characterizations of disconnected space were given by using the properties of correlative-type disconnected space and disconnected space and relationships between them.