G-continuous mappings and G-quotient mappings(G连续映射与G商映射)

As a generalization of the usual convergence in topological spaces, a method G on a set X is a function G:cGX→X defined on a subset cGX which is constituted by some sequences in X. In this paper, we mainly study the G-continuous mappings and the G-quotient mappings determined by G-methods and their connections with continuous mappings and quotient mappings in topological spaces. At the same time, we also discuss some properties of G-open mappings and G-closed mappings, and unify some results of several important convergence of sequences involving continuous mappings and quotient mappings.作为拓扑空间通常收敛性的拓展，在集合X上的方法是定义于X的由某些序列组成的集cGX到X的函数G:cGX→X。主要研究了由G方法确定的G连续映射与G商映射，及其与拓扑空间的连续映射、商映射的联系，同时讨论了G开映射与G闭映射的一些性质，统一了几类重要的序列收敛性关于连续映射及商映射的一些结果。