2010/06/24 by Hüseyi̇n Çakallı, Huseyin Cakalli, Cakalli, Huseyin · 1 citation
Mathematics · #22A05 #40J05 #54A05 #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:22A05 #msc:40J05 #msc:54A05
paper · pdf · doi:10.48550/arxiv.1006.4706
This paper has been withdrawn by the author. I withdraw my paper due to the acceptance in the journal "Computers & Mathematics with Applications"
openalex publication_date 2010/06/24 · arxiv created 2010/11/11 · arxiv updated 2010/11/12 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
A function f on a topological space is sequentially continuous at a point u if, given a sequence (xn), lim xn=u implies that lim f(xn)=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.