Volume 23 , Issue 3 , PP: 148-153, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Eman Almuhur 1 * , Husam Miqdad 2 , Manal Al-labadi 3 , Mohammad I. Idrisi 4
Doi: https://doi.org/10.54216/IJNS.230313
In the final years of the 20th century, the notion of generalized topological spaces was introduced, marking a significant shift in the field of topology. This paper focuses on a subset of ℘(X) on a non-empty set X that is closed under arbitrary unions, defining a generalized topology and subsequently a generalized topological space (GTS) denoted by (X,μ). Within this framework, we explore the concept of Noetherian generalized topological spaces and delve into the properties of μ-L-closed subsets within the Noetherian GTS. The investigation reveals that subspaces of a μ-Noetherian GTS X, with the induced topology, inherit the μ-Noetherian property and exhibit finitely many non-empty μ-irreducible components. Furthermore, the study extends to the analysis of hereditary properties, regular 〖μ-G〗_δ, 〖μ-d〗_δ, μ-irreducible L-closed subsets, and the product properties of μ-L-closed subsets under (μ,μ')-continuous functions. We also establish the closure property of finite unions in μ-Noetherian GTS and clarify the homeomorphic nature of μ-Noetherian GTS (X,μ) to itself.
Keywords: GTS, &mu , -Noetherian, (&mu , ,&mu , ')-continuous function, fuzzy topology, neutrosophic topology.
[1] Császár A. Generalized open sets in generalized topologies. Acta mathematica hungarica. 2005 Jan 1; 106. DOI: http://doi.org/10.1007/s10474-005-0005-5
[2] Almuhur E, Al-Labadi M, Shatarah A, AbuHijleh EA, Khamis S. On $\mu $-L-closed, q-compact and q-Lindelöf spaces in generalized topological spaces. International Journal of Nonlinear Analysis and Applications. 2022 Feb 1; 13(1): 3853-3859. DOI: https://doi.org/10.22075/ijnaa.2022.6181
[3] Hdeib HZ, Pareek CM. On spaces in which Lindelöf sets are closed. Q & A in General Topology. 1986; 4(1): 986.
[4] Makai Jr E, Peyghan E, Samadi B. Weak and strong structures and the T 3.5 property for generalized topological spaces. Acta Mathematica Hungarica. 2016 Oct; 150(1):1-35. DOI: https://doi.org/10.1007/s10474-016-0653-7
[5] Sarsak M. Weak separation axioms in generalized topological spaces. Acta Mathematica Hungarica. 2011 Apr 1; 131. DOI: http://doi.org/10.1007/s10474-010-0017-7
[6] Noorie NS, Bala R. On a natural transformation between generalized topologies and strongly generalized interior operators. Global Journal of Pure and Applied Mathematics. 2017; 13(7): 3301-3305.
[7] S. Gunavathy, R. Alagar, A. Iampan and V. Govindan. "Nano I-connectedness and Strongly Nano I-connectedness in Nano Topological Spaces". Mathematics and Statistics, 10(5), pp. 1111 - 1115. DOI: 10.13189/ms.2022.100521
[8] Saleh H, Asaad BA, Mohammed R. Bipolar soft limit points in bipolar soft generalized topological spaces. Mathematics and Statistics. 2022; 10(6): 1264-1274. DOI: http://doi.org/10.13189/ms.2022.100612
[9] Tyagi BK. On generalized closure operators in generalized topological spaces. International Journal of Computer Applications. 2013 Jan 1; 82(15).
[10] Császár Á. Further remarks on the formula for γ-interior. Acta Mathematica Hungarica. 2006 Dec 17; 113(4): 325-332. DOI: https://doi.org/10.1007/s10474-006-0109-6
[11] Min WK. A note on quasi-topological spaces. Honam Mathematical Journal. 2011; 33(1): 11-17. DOI: https://doi.org/10.5831/HMJ.2011.33.1.011
[12] Tyagi BK, Chauhan H. On generalized closed sets in generalized topological spaces. Cubo (Temuco). 2016; 18(1): 27-45. DOI: http://dx.doi.org/10.4067/S0719-06462016000100003
[13] Tyagi B, Chauhan H. On some separation axioms in generalized topological spaces. Questions and answers in general topology. 2018; 36(1): 9-29.
[14] Min WK. Results on strong generalized neighborhood spaces. The Pure and Applied Mathematics. 2008; 15(3): 221-227.
[15] Min WK. On strong generalized neighborhood systems and sg-open sets. Communications of the Korean Mathematical Society. 2008; 23(1): 125-131. https://doi.org/10.4134/CKMS.2008.23.1.125Equations. In International Conference on Mathematics and Computations (pp. 15-24). Singapore: Springer Nature Singapore, (2022).
