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Journals / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

G-convergence and G-sequential spaces

Shanza Behram(ERCIYES UNIVERSITY)0000-0003-2244-7404
Osman Mucuk(ERCIYES UNIVERSITY)0000-0001-7411-2871
Pages
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Publication Date
2025-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, examples of $G$-sequential spaces associated with $G$-methods are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:Then, $G$-sequential continuity is investigated, and the relations between $G$-continuous and $G$-sequentially continuous functions are determined.
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Conclusion & Impact:Finally, examples of $G$-sequential spaces associated with $G$-methods are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:G-method · G-convergence · G-sequential space

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.

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Cite This Article

Behram, S., Mucuk, O. (2025). G-convergence and G-sequential spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1585422

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