G连通性

G-connectedness

集X上的G方法是定义于X的某序列集到X上的一个函数,借助G方法引入G隔离集,在集上给出G连通子集的概念,获得G连通集的等价刻画,并讨论了连通性、序列连通性和G连通性之间的关系,把序列连通性及满足第一可数公理的Hausdorff拓扑群中G连通性的结果推广到一般集上的G连通性.

A G-method on a set X is a function defined on a subset of X-valued sequences to the set X.This paper introduces the notion of G-separated sets through G-methods.It defines G-connected subsets,obtain some characterizations of G-connected sets and discusses the relationships among connectedness,sequential connectedness and G-connectedness.The author investigates several properties of G-connected subsets,and extends sequential connectedness and G-connectedness on Hausdorff topological groups which satisfy first countability axiom to G-connectedness on an arbitrary set.