On G-Continuity

Abstract

A function $f$ on a topological space is sequentially continuous at a point $u$ if, given a sequence $(x_n)$, $\lim x_n=u$ implies that $\lim f(x_n)=f(u)$. This definition was modified by Connor and Grosse-Erdmann for real functions by replacing $lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. In this paper, we extend this definition to a topological group $X$ by replacing $G$ a linear functional with an arbitrary additive function defined on a subgroup of the group of all $X$-valued sequences and not only give new theorems in this generalized setting but also obtain theorems which are not appeared even for real functions so far.

This paper has been withdrawn by the author. I withdraw my paper due to the acceptance in the journal "Computers & Mathematics with Applications"