Neutrosophic Nano ɡ#ψ-Compact, Connected, Regular and Normal Spaces in Neutrosophic Nano Topological Spaces
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Abstract
Smarandache introduced neutrosophic sets as an extension of fuzzy and intuitionistic fuzzy sets to manage the imprecise, incomplete, and inconsistent information often encountered in real-world contexts. A neutrosophic set is characterized by three parameters: truth value, indeterminacy value, and falsity value. Building upon this framework, Salama formulated neutrosophic topological spaces. The concept of a Neutrosophic Nano Topological Space merges the principles of neutrosophic sets with nano topology to address uncertainty, indeterminacy, and vagueness in systems or structures of extremely small or fine-grained scale. In this paper, we introduce the notions of spaces, countably spaces, spaces, sets, spaces, spaces, spaces, spaces, strongly spaces, spaces, and strongly spaces by using sets and sets in Neutrosophic nano topological spaces. We study their basic properties and fundamental characteristics in
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References
Acikegoz, Ahu, & Esenbel, Ferhat (2020). An Approach to Pre-Separation Axioms in Neutrosophic Soft Topological Spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., Volume 69, Number 2, pp.1389 – 1404.
Al-Hamido, Riad K. (2020). On Neutrosophic Crisp Supra Bi-Topological Spaces”’, International Journal of Neutrosophic Science, Volume 4, Issue 1, pp.36-46.
Amarendra, Babu V. & Aswini, J. (2021). Separation Axioms in Supra Neutrosophic crisp Topological Spaces, Advances and Applications in Mathematical Sciences, Volume 20, Issue 6, pp. 1115 – 1128.
Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets Systems, 20, pp.87-96.
Atanassov, K. & Stoeva, S., Intuitionistic fuzzy sets, In Proceedings of the Polish Symposium on Interval and Fuzzy Mathematics, Poznan, Poland, 26-29 August 1983, pp.23-26.
Bageerathi, K. & Puvaneswari, P. Jeya (2019). Neutrosophic Feebly Connectedness and Compactness, IOSR Journal of Polymer and Textile Engineering (IOSR-JPTE), Volume 6, Issue 3, pp. 07 – 13.
Benchalli, S.S., Patil, P.G. & Dodamani, Abeda S. (2017). Some Properties of Soft β-Compact and Related Soft Topological Spaces, Italian Journal of Pure and Applied Mathematics, No.38, pp. 487 – 496.
Chang, C.L. (1968). Fuzzy Topological Spaces, Journal of Mathematical Analysis and Applications, 24, pp. 182 – 190.
Coker, Dogan (1997). An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, Vol 88, No.1, pp. 81 – 89.
Das, Sapan Kumar & Edalatpanah, S.A. (2020). A new ranking function of triangular neutrosophic number and its application in integer programming, International Journal of Neutrosophic Science, Volume 4, Issue 2, pp. 82 - 92.
Dhavaseelan, R. & Jafari, S. (2017). Generalized Neutrosophic Closed Sets, New Trends in Neutrosophic Theory and Applications, Vol. II, pp. 261 – 273.
Evanzalin, Ebenaniar P. & Jude, Immaculate H., & Bazil, Wilfred C. (2018). On Neutrosophic b-open sets in Neutrosophic topological space, International Conference on Applied and Computational Mathematics, IOP Conf. Series: Journal of Physics: pp. 1 – 5.
Imran, Hatem Qays, Smarandache, F., Al-Hamido, Riad K. & Dhavaseelan, R. (2017). On Neutrosophic Semi Alpha Open Sets, Neutrosophic Sets and Systems, Vol. 18, pp. 37 – 42.
Iswarya, P. & Bageerathi, Dr. K. (2019). A Study on Neutrosophic Generalized Semi-Closed Sets in Neutrosophic Topological Spaces, Journal of Engineering Technologies and Innovative Research (JETIR), Volume 6, Issue 2, pp. 452 – 457. www.jetir.org
Jeevitha, R., Parimala, M., & Kumar, R. Udhaya (2019). Nano Aψ-Connectedness and Compactness in Nano Topological Spaces, International Journal of Research Technology and Engineering, Volume 8, Issue 2, 4 pages.
Krishnaprakash, S., Ramesh, R. & Suresh, R. (2018). Nano-Compactness in Nano Topological Space, International Journal of Pure and Applied Mathematics, Volume 119, No. 13, pp. 107 – 115.
Krishnaprakashi, K., & Chandrasekar, S. (2020). Neutrosophic bg-closed Sets and their Continuity, Neutrosophic Sets and Systems, Vol. 36, pp. 108 – 120.
Maheshwari, Babu C. and Chandrasekar, S. (2019). Neutrosophic GB-Closed Sets and Neutrosophic GB-Continuity, Neutrosophic Sets and Systems, Vol. 29, pp. 89 – 100.
Mary, Margaret A., & Trinita, Pricilla M. (2018). Neutrosophic Vague Generalized PreConnectedness in Neutrosophic Vague Topological Space, International Journal of Mathematics Trends and Technology (IJMTT), Volume 58, Issue 2, pp. 85 – 93.
Mehmood, A., Nadeem, F., Nordo, G., Zamir, M., Park, C., Kalsoom, H., Jabeen, S., & Khan, M. I. (2020). Generalized Neutrosophic Separation Axioms in Neutrosophic Soft Topological Spaces, Neutrosophic Sets and Systems, Volume 32, pp. 38 – 51.
Molodtsov, D. A. (1999). Soft set theory-first results, Comput. Math. Appl. 37, pp. 19 – 31.
Mullai, M., Sangeetha, K., Surya, R., Madhan Kumar, G., Jeyabalan, R., and Broumi, S. (2020). A Single Valued Neutrosophic Inventory Model with Neutrosophic Random Variable, International Journal of Neutrosophic Science, Volume 1, Issue 2, pp.52 – 63.
Al-Nafee, Ahmed B., Al-Hamido, Riad K. & Smarandache, Florentin (2019). Separation Axioms in Neutrosophic Crisp Topological Spaces, Neutrosophic Sets and Systems, Vol. 25, pp. 25 – 32.
Nandhini, T., and Vigneshwaran, M., (2019). On ????????????#???? -continuous and ????????????#???? -irresolute functions in neutrosophic topological spaces, International Journal of Recent Technology and Engineering, Volume 7, 6, 1097-1101.
Nandhimi, T., and Vigneshwaran, (2019). ????????????#???? -Open map, ????????????#???? -closed map, and ????????????#???? -homeomorphism in neutrosophic topological spaces, Neutrosophic Sets and Systems, Volume 29, pp. 187 – 186.
Nandhini, T. & Vigneshwaran, M. (2019). Nαg#ψ-closed sets in neutrosophic topological spaces, American International Journal of Research in Science, Technology, Engineering and Mathematics, Special issue of 2nd International Conference on Current Scenario in Pure and Applied Mathematics, 3rd January 2019, pp. 370 – 373.
Nandhini, T. and Vigneshwaran, M. (2020). On Neutrosophic nano αɡ#ψ-closed sets in neutrosophic nano topological spaces, International Journal of Neutrosophic Science (IJNS), Vol. 5, No. 2, pp. 67 – 71.
Nandhini, T., Banu, Dr. M. Nazreen, Savithiri, Dr. D., Devi, Pandima, Dr. J., Rajalakshmi, R., Suganthi, Dr. G., Brindha, Dr. R. (2025). Neutrosophic Nano Topology: An Analysis of Neut.nano αg#ψ-Open and Closed Functions and Their Properties, Advances in Nonlinear Variational Inequalities, Vol 28 No. 4s, pp. 344 – 350.
Parimala, M., Jeevitha, R., Jafari, S., Samarandache, F., & Karthika, M. (2018). Neutrosophic Nano αψ-Closed Sets in Neutrosophic Nano Topological Spaces, Journal of Advanced Research in Dynamical & Control Systems, Vol. 10, 10-Special Issue, pp. 523 – 531.
Parimala, M., Karthika, M., Jafari, S., Smarandache, F., & Udhayakumar, R. (2019), Neutrosophic Nano ideal topological structure, Neutrosophic Sets and Systems, Vol. 24, pp. 70 – 76.
Parimala, M., Karthika, K., Smarandache, F., & Broumi, Said (2020). On αw-closed sets and their connectedness in terms of neutrosophic topological spaces, International Journal of Neutrosophic Science, Volume 2, Issue 2, PP. 82 – 88.
Parimala, M., Jeevitha, R., Jafari, S., Samarandache, F., & Karthika, M. (2018). Neutrosophic nano αψ-closed sets in neutrosophic nano topological spaces, Journal of Advanced Research in Dynamical and Control Systems, Vol 10, pp. 523 – 531.
Pawlak, Z. (1982). Rough Sets, International Journal of Computing and Information Sciences, 11 (5), pp.341-356.
Salama, A. A. & Alblowi, S. A. (2012). Neutrosophic sets and neutrosophic topological spaces, IOSR Journal of Mathematics, 3(4), pp. 31 – 35.
Salama, A. A., Smarandache, Florentin, & Kromov, Valeri (2014). Neutrosophic Closed Sets and Neutrosophic Continuous Functions, Neutrosophic Sets and Systems, Vol. 4, pp. 4 – 8.
Al-Shami, Tareq M., Mhemdi, Abdelwahab, Rawshdeh, Amani A., & Al-Jarrah, Heyam H. (2021). Soft version of compact and Lindelof spaces using soft somewhere dense sets, AIMS Mathematics, 6(8), pp. 8064–8077.
Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability; American Research Press: Rehoboth, NM, USA.
Smarandache, F. (2002). Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup. NM 87301, USA.
Thivagar M.L., & Richard C. (2013). On nano forms of weakly open sets. Int J Math Stat Invent;1(1): pp. 31–37. https://ijmsi.org/Papers/Version.1/E0111031037
Thivagar, M. Lellis, Jafari, Saeid, Devi, V. Sutha, Antonysamy, V. (2018). A novel approach to nano topology via neutrosophic sets, Neutrosophic Sets and Systems, Vol. 20, pp. 86 – 94.
Turnali, N. & Coker, D. (2000). Fuzzy Connectedness in Intuitionistic Fuzzy Topological Spaces, Fuzzy Sets and Systems, 116, pp. 369 – 375.
Vijayalakshmi, R. & Mookambika, A. P. (2020). Properties of neutrosophic nano semi-open sets, Malaya Journal of Mathematika, Vol. 8, No. 4, pp. 1851 – 1858.
Vadivel, A., Sundar, C. John, Kirubadevi, K., & Tamilselvan, S. (2022). More on Neutrosophic Nano Open Sets, International Journal of Neutrosophic Science (IJNS), Vol. 18, No. 04, PP. 204-222.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, Vol. 8, pp. 338 – 353.