On G-quotient spaces

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.