On G-Sequential Continuity

TL;DR

This paper explores the concept of G-sequential continuity in topological groups, extending previous notions and providing new insights that also apply to real functions, with a focus on properties like compactness and continuity.

Contribution

It advances the understanding of G-sequential continuity in topological groups, introducing new results that generalize and deepen previous work, including applications to real functions.

Findings

Extended G-sequential continuity to broader classes of topological groups.

Introduced new results on G-sequential compactness and continuity.

Most results are also applicable to real functions, broadening their relevance.

Abstract

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.