On G-Sequential Continuity

Details On G-Sequential Continuity On G-Sequential Continuity

2011-12-22

arxiv.org/abs/1201.1795v1

Mathematics

General Topology

15 pages, Research Paper, arXiv admin note: substantial text overlap with arXiv:1006.4706 and arXiv:1105.2203 by other author

Scientific paper

Let $X$ be a first countable Hausdorff topological group. The limit of a sequence in $X$ defines a function denoted by $lim$ from the set of all convergence sequences to $X$. 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. \c{C}akall{\i} extended the concept to topological group setting and introduced the concept of $G$-sequential compactness and investigated $G$-sequential continuity and $G$-sequential compactness in topological groups. In this paper we give a further investigation of $G$-sequential continuity in topological groups most of which are also new for the real case.

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