Advancing Neutrosophic Topology through b-Open Sets and their Application to Neutrosophic b-Compact Spaces
DOI:
https://doi.org/10.54172/t7dmaa92Keywords:
neutrosophic b-open sets, neutrosophic subspaces, neutrosophic b -compact spaces.Abstract
The main objective of this study is to develop a neutrosophic topology by applying topological mechanisms to establish an induced neutrosophic topology and new topological spaces known as neutrosophic subspaces. In addition, we apply specific topological tools to neutrosophic concepts (open neutrosophic sets of type b) and study the properties of this type of neutrosophic openness. The resulting space, which does not satisfy the three topological conditions but is limited to a supra topology, is called a neutrosophic b supra topological space, and we investigate its main properties. Based on this framework, the concept of b neutrosophic compactness is developed as a natural generalization of compactness in neutrosophic spaces. We establish that every b-compact neutrosophic space is a compact neutrosophic space, but the converse is not true. The research also examines how b-compactness behaves under various mappings, such as continuous and open neutrosophic functions, such as connected and open neutrosophic functions. Furthermore, the research also shows that every neutrosophic supra b-compact space is neutrosophic supra compact and neutrosophic b-compact. The results show that neutrosophic b-compactness serves as a flexible and powerful tool capable of describing and explaining real-world phenomena that are predominantly characterized by uncertainty. Accordingly, this approach reinforces the foundations of neutrosophic topology, which increases its applicability in data analysis, leading to decisions that are more precise.
References
Al Amin, E. (2022). On Neutrosophic Pre-Approximation Space.
Andrijević, D. (1996). On $ b $-open sets. Matematički Vesnik, 48(1–2), 59-64.
Arokiarani, I., Dhavaseelan, R., Jafari, S., & Parimala, M. (2017). On some new notions and functions in neutrosophic topological spaces. Neutrosophic sets and systems, 16(1), 4.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.
Das¹, R., & Tripathy, B. C. (2020). Neutrosophic multiset topological space. Neutrosophic Sets and Systems, Book Series, Vol. 35, 2020. An International Book Series in Information Science and Engineering, 142.
Das, R., Smarandache, F., & Tripathy, B. C. (2020). Neutrosophic fuzzy matrices and some algebraic operations. Infinite Study.
Dey, S., & Ray, G. C. (2023). Pre-separation Axioms in Neutrosophic Topological Spaces. International Journal of Neutrosophic Science, 22(02), 15-28. https://doi.org/https://doi.org/10.54216/IJNS.220202
Dhar, R. (2023). Compactness and neutrosophic topological space via grills. Neutrosophic Systems with Applications, 2, 1-7. https://doi.org/https://doi.org/10.61356/j.nswa.2023.6
Ebenanjar, P. E., Immaculate, H. J., & Wilfred, C. B. (2018). On Neutrosophic b-open sets in Neutrosophic topological space. Journal of Physics: Conference Series, 1139(1), 012062. https://doi.org/10.1088/1742-6596/1139/1/012062
Gupta, M., & Gaur, M. (2018). C-compactness via grills. World Scientific News, 113.
Imran, Q. H., Smarandache, F., Al-Hamido, R. K., & Dhavaseelan, R. (2017). On Neutrosophic semi alpha open sets.
Iswarya, P., & Bageerathi, K. (2016). On neutrosophic semi-open sets in neutrosophic topological spaces. Infinite Study.
Jayaparthasarathy, G., Flower, V. L., & Dasan, M. A. (2019). Neutrosophic supra topological applications in data mining process. Infinite Study.
Pal, G., Tripathy, B. C., & Dhar, R. (2022). On continuity in minimal structure neutrosophic topological space. Neutrosophic sets and systems, 51, 360-370.
Roy, B., & Mukherjee, M. (2007). On a type of compactness via grills. Matematichki Vesnik, 59(3), 113-120.
Salama, A., & Alblowi, S. (2012). Generalized neutrosophic set and generalized neutrosophic topological spaces. Infinite Study. https://doi.org/DOI:10.5923/j.computer.20120207.01
Salama, A., & Alblowi, S. A. (2012). Neutrosophic set and neutrosophic topological spaces.
Salama, A., Smarandache, F., & Alblowi, S. (2014). New neutrosophic crisp topological concepts.
Salama, A., Smarandache, F., & Kromov, V. (2014). Neutrosophic closed set and neutrosophic continuous functions. Infinite Study.
Singal, M., & Singal, A. R. (1968). Almost-continuous mappings. Yokohama Mathematical Journal= 横濱市立大學紀要. D 部門, 数学, 16(2), 63-73.
Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis.
Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition): Neutrsophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (3rd Edition). American Research Press. https://books.google.com.ly/books?id=qIzdBAAAQBAJ
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/https://doi.org/10.1016/S0019-9958(65)90241-X
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