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On α-δ^*-open sets in topological space | ||
| Journal of Hyperstructures | ||
| دوره 15، شماره 1، شهریور 2026، صفحه 91-98 اصل مقاله (1.61 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2026.16214.1060 | ||
| نویسندگان | ||
| K Perarasan* 1؛ B. MOHAMED HARIF2؛ A. DINESH KUMAR3 | ||
| 1Assistant professor Department of mathematics Annai Vailankanni Arts and Science College Thanjavur | ||
| 2Department of Mathematics, Government Arts College (Affiliated to Bharathidasan University), Tiruchirappalli -02, Tamilnadu, India. | ||
| 3Department of Mathematics, Khadir Mohideen College (Affiliated to Bharathidasan University), Adirampattinam, Tamil Nadu, India | ||
| چکیده | ||
| In the study of topological spaces, the concept of α-δ^*-open sets introduces a generalized framework for defining openness beyond traditional topological notions. An α-δ^*open open set is characterized by its adherence to specific conditions denoted by parameters α and δ^*, influencing its properties within the topology of a space. This investigates fundamental operations on α-δ^*-open sets, aiming to establish their behavior under set-theoretic operations and topological constructions. Key operations include union, intersection, complementation, and their implications for maintaining α-δ^*-open openness. Moreover, the abstract explores the interplay between α-δ^*-open sets and classical topological concepts such as interior, closure, and boundary, elucidating how these operations interacts within the broader framework of abstract topology. By examining these operations, this contributes to a deeper understanding of α-δ^*open sets and their role in extending traditional topological principles, thereby enriching the theoretical foundations of topology. | ||
| کلیدواژهها | ||
| α-δ^*-open set؛ τ_(α-γ^* )-int(A)؛ τ_(α-γ^* )-cl(A) | ||
| مراجع | ||
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[1] N. Levine, Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70(1), 36-41. [2] Njastad, O. (1965). On some classes of nearly open sets. Pacific journal of mathematics, 15(3), 961-970. [3] Park, J. H., Lee, B. Y., & Son, M. J. (1997). On δ-semiopen sets in topological spaces. J. Indian Acad. Math, 19(1), 59-67. [4] Krishnan, G. S. S., & Balachandran, K. (2006). On a class of γ-preopen sets in a topological space. East Asian Math. J, 22(2), 131-149. [5] Latif, R. M. (2006). Characterizations and applications of gamma-open sets. Soochow Journal of Mathematics, 32(3), 369. [6] Khader, S. M. (2019). New Forms of Continuity ( δ-e-Continuous and Contra δ-e-Continuous). [7] Chattopadhyay, C. (2005). On strongly pre-open sets and a decomposition of continuity. Matematnykn Bechnk, 57, 121-125. [8] Van An, T., Cuong, D. X., & Maki, H. (2008). On Operation Preopen Sets in Topological Space. Scientiae Mathematicae Japonicae, 21, 241-260. [9] Scheers, J. M. (2011). An exploration of semi-open sets in topological spaces (Master’s thesis, Stephen F. Austin State University). [10] Rekha, T. I. K. (2012). Applications of* b-open Sets and** b-open Sets in Topological Spaces. Annals of pure and Applied Mathematics, 1(1), 44-56. [11] Khader, S. M. (2016). New forms of continuity ( δ − α-continuous and contra δ − α-continuous). [12] Khader, S. M. (2019). New Forms of Continuity ( δ-e-Continuous and Contra δ-e-Continuous). [13] Ozel, Cenap, Shumrani Al, Aynur Keskin Kaymakci, Choonkil Park, and Dong Yun Shin. (2021). On δ b-open continuous functions. AIMS Mathematics 6, no. 3: 2947-2955. [14] Shanmugapriya, H., and K. Sivakamasundari. (2024). ” ρ-Open Sets in Topological Spaces.” Southeast Asian Bulletin of Mathematics 48, no. 1, 121-128. | ||
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