G-Sequential Convergences in Submethods

Abstract

 In  a  topological space $X$, limits of sequences give us  a set valued function defined for convergent sequences and taking the subsets of $X$ as values.   Then sequential versions of  some topological  notions are generalised to $G$-methods by replacing $\lim$ function with any map $G$. A $G$-method enables us to define a variety of convergence $G_s$ called $G$-sequentially convergence and   gives rise to a method $G_Y$ on a subset $Y\subseteq X$ called  submethod.    In this paper,  we consider  $G$-sequentially methods or $G_s$-methods  created by $G$-methods and search the reducibility of such methods to the subsets with  some properties and characterisations.