On $G$-quotient spaces

Abstract

The $G$-convergence of sequences is a general method of convergence of sequences in topological spaces. The operations related to $G$-methods in topological spaces have been studied. In this paper, we discuss $G$-quotient spaces, which are a class of generalized quotient spaces, and obtain the relationship between $G$-quotient topology and the largest topology of the range that makes the mapping be $G$-continuous. These results can be applied to statistical convergence and ideal convergence in topological spaces.