G-convergence and G-sequential spaces

Year 2025, Volume: 54 Issue: 6, 2326 - 2334, 30.12.2025

Shanza Behram , Osman Mucuk

https://doi.org/10.15672/hujms.1585422

Abstract

In this paper, for a method $G$ on a set $X$, we consider $G$-convergence and $G$-sequential convergence; we analyse the distinction between them with some counterexamples. Then, $G$-sequential continuity is investigated, and the relations between $G$-continuous and $G$-sequentially continuous functions are determined. Moreover, $G$-sequential spaces are introduced and studied. Finally, examples of $G$-sequential spaces associated with $G$-methods are given.

Keywords

G-method , G-convergence , G-sequential space

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