1
Department of Mathematics, Applied Science Private University, Amman, Jordan
(e_almuhur@asu.edu.jo)
2
Department of Basic Science / Scientific, Applied Science Private University, Amman, Jordan
( hmiqdad@hotmail.com)
3
Department of Mathematics, University of Petra, Amman, Jordan
(manal.allabadi@uop.edu.jo)
4
Department of Mathematics, Chandigarh University, Punjab, India
(mhdimranidrisi@gmail.com)
Abstract :
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 :
Keywords: GTS , μ-Noetherian , (μ , μ')-continuous function , fuzzy topology , neutrosophic topology.
References :
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| Style | # |
|---|---|
| MLA | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi. "μ-L-Closed Subsets of Noetherian Generalized Topological Spaces." International Journal of Neutrosophic Science, Vol. 23, No. 3, 2024 ,PP. 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |
| APA | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi. (2024). μ-L-Closed Subsets of Noetherian Generalized Topological Spaces. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |
| Chicago | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi. "μ-L-Closed Subsets of Noetherian Generalized Topological Spaces." Journal of International Journal of Neutrosophic Science, 23 no. 3 (2024): 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |
| Harvard | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi. (2024). μ-L-Closed Subsets of Noetherian Generalized Topological Spaces. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |
| Vancouver | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi. μ-L-Closed Subsets of Noetherian Generalized Topological Spaces. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 3 ): 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |
| IEEE | Eman Almuhur, Husam Miqdad, Manal Al-labadi, Mohammad I. Idrisi, μ-L-Closed Subsets of Noetherian Generalized Topological Spaces, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 3 , (2024) : 148-153 (Doi : https://doi.org/10.54216/IJNS.230313) |