About G-convergence and G-sequentially convergence
Abstract
In this paper we will discuss the similarities and differences for some topological properties in $G$-continuity and $G$-sequential continuity.
In particular we will illustrate the ways in which these notions agree and are divided in some topological properties by looking at their definitions, characteristics, and implications. We will use examples from the literature \cite{counterexample} to distinguish between G-continuity and G-sequential continuity. Moreover, we will prove that these two kinds of continuity produce different outcomes and broaden the notion of the G-method in topological spaces.
Keywords
References
- J. Connor, K.-G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. , 33(1) (2003), 93-121.
- S. Lin, L. Liu, G-methods, G-spaces and G-continuity in topological spaces, Topology Appl., 212 (2016), 29-48.
- H. Çakallı, Sequential definitions of compactness, Appl. Math. Lett., 21 (6) (2008), 594-598.
- O. Mucuk, H. Çakallı, G-sequentially connectedness for topological groups with operations, Filomat, 32(3) (2018), 1079-1089.
- Mucuk, O. and T. Şahan, On G-sequential Continuity, Filomat, 28 (6) (2014), 1181-1189.
- S. Behram and O. Mucuk, About varieties of G-sequential methods, G-hulls and G-closures, Proceedings of International Mathematical Sciences, 5 (2) (2023), 81-86.
- H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett., 25 (3) (2012), 461-465.
- H. Çakallı, and O. Mucuk, On connectedness via a sequential method, Revista de la Unión Matemática Argentina, 54 (2) (2013), 101-109.
Details
Primary Language
English
Subjects
Applied Mathematics (Other)
Journal Section
Research Article
Publication Date
January 3, 2026
Submission Date
December 9, 2024
Acceptance Date
December 31, 2024
Published in Issue
Year 2025 Volume: 7 Number: 2
APA
Mucuk, O., & Behram, S. (2026). About G-convergence and G-sequentially convergence. Proceedings of International Mathematical Sciences, 7(2), 40-45. https://doi.org/10.47086/pims.1598531
AMA
1.Mucuk O, Behram S. About G-convergence and G-sequentially convergence. PIMS. 2026;7(2):40-45. doi:10.47086/pims.1598531
Chicago
Mucuk, Osman, and Shanza Behram. 2026. “About G-Convergence and G-Sequentially Convergence”. Proceedings of International Mathematical Sciences 7 (2): 40-45. https://doi.org/10.47086/pims.1598531.
EndNote
Mucuk O, Behram S (January 1, 2026) About G-convergence and G-sequentially convergence. Proceedings of International Mathematical Sciences 7 2 40–45.
IEEE
[1]O. Mucuk and S. Behram, “About G-convergence and G-sequentially convergence”, PIMS, vol. 7, no. 2, pp. 40–45, Jan. 2026, doi: 10.47086/pims.1598531.
ISNAD
Mucuk, Osman - Behram, Shanza. “About G-Convergence and G-Sequentially Convergence”. Proceedings of International Mathematical Sciences 7/2 (January 1, 2026): 40-45. https://doi.org/10.47086/pims.1598531.
JAMA
1.Mucuk O, Behram S. About G-convergence and G-sequentially convergence. PIMS. 2026;7:40–45.
MLA
Mucuk, Osman, and Shanza Behram. “About G-Convergence and G-Sequentially Convergence”. Proceedings of International Mathematical Sciences, vol. 7, no. 2, Jan. 2026, pp. 40-45, doi:10.47086/pims.1598531.
Vancouver
1.Osman Mucuk, Shanza Behram. About G-convergence and G-sequentially convergence. PIMS. 2026 Jan. 1;7(2):40-5. doi:10.47086/pims.1598531
