On Gα -open sets

Ali, Tabarak A.; Esmaeel, Rana B.

doi:10.47974/JIM-1658

Open Access Research Article

On Gα -open sets

^*Tabarak A. AliCorresponding authortabarakayad314@gmail.comDepartment of MathematicsCollege of Education for Pure Science (Ibn Al- Haitham)University of BaghdadBaghdad, IraqView full profile → , Rana B. EsmaeelRana.b.i@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al- Haitham)University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1627–1633Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1658XML

Published Online:: 01 Nov 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1658
Pages:: 1627–1633

Abstract

The new concepts in grill topological spaces are investigated in this study by employing specified sets in which the α-open sets are defined and grill topological spaces. Properties of this set and certain relationships are studied, examining a group of functions, like open, closed, and continuous functions, determining their relation with each other and giving examples and properties associated with this set. This shall serve as the beginning of examining numerous topological properties with this set.

Keywords

Grill α - o sets Gα -o set α-c sets Gα -of Gα -c f

Subject Classifications

Primary 54C10Secondary 90C51

References

[1] G. Choquet, Sur les notions de filtre et grill, Compt. Rend. Acad. Sci. Paris 224, 171–173 (1947).
[2] B. Roy and M.N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math. 33(4), 771–786 (2007).
[3] M.O. Mustafa and R.B. Esmaeel, Some properties in grill-topological open and closed sets, J. Phys. Conf. Ser. 1897(1), 012038 (2021).
[4] Mahmood, Ali J., and A. I. Naser. “Connectedness via Generalizations of Semi-Open Sets.” Ibn Al-Haitham Journal For Pure and Applied Sciences 35.4 (2022).
[5] N. A. Jabbar and A. I. Nasir, Some Types of Compactness in Bitopological spaces, Ibn Al-Haitham Journal for Pure and Applied Science, 23(l) (2010).
[6] O. Njastad, “ On some Classes of Nearly Open sets”, Pacific Journal of Mathematics, 15(3) (1965).
[7] A. Al-Omari and T. Noiri, Decompositions of continuity via grills, Jordan J. Math. Stat. 4(1), 33- 46 (2011).
[8] Shamkhi, M., & Kadhem, H. H. : On Soft Pre-Compact Maps. Wasit Journal of Computer and Mathematics Sciences, 1(2), 78-95 (2022).‏
[9] A. Kalavathi & G. Sai Sundara Krishnan. Soft g* closed and soft g*open sets in soft topological spaces, Journal of Interdisciplinary Mathematics, 19:1, 65-82 (2016), DOI: 10.1080/09720502.2015.1103110.
[10] Anabel E. Gamorez & Sergio R. Canoy Jr. : Subbasic open sets in graphs generated by monophonic eccentric neighborhoods, Journal of Discrete Mathematical Sciences and Cryptography, 24:7, 1989-2000 (2021), DOI: 10.1080/09720529.2021.1923922.

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