Mathematics – General Topology
Scientific paper
2010-06-24
Mathematics
General Topology
This paper has been withdrawn by the author. I withdraw my paper due to the acceptance in the journal "Computers & Mathematics
Scientific paper
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.
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