2011/05/11 by Hüseyi̇n Çakallı, Huseyin Cakalli, Cakalli, Huseyin · 2 citations
Computer Science · Mathematics · #22A05} #40J05 #54A05 #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:40J05 #msc:54A05 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1105.2203
This paper has been withdrawn by the author since it will be published in Applied Mathematics Letter which is not open acces journal
openalex publication_date 2011/05/11 · arxiv created 2012/01/20 · arxiv updated 2012/01/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
A topological group X is called connected if the only subsets which are both open and closed are the whole space X and the null set ∅. A subset of a topological group is connected if the subspace is connected. We say that a subset A of X is G-sequentially connected if the only subsets of A which are both G-sequentially open and G-sequentially closed, with respect to the relative G-sequentially open and G-sequentially closed subsets of A, are open and closed subsets of A are A and the null set, ∅. We investigate the impact of changing the definition of convergence of sequences on the structure of sequential connectedness of subsets of X via sequential closure of sets in the sense of G-sequential closure. Sequential connectedness for topological groups is a special case of this generalization when G = lim.