Volume 6 , Issue 2 , PP: 38-48, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
C. John Sundar 1 * , A. Vadivel 2
Doi: https://doi.org/10.54216/JNFS.060204
In this paper the concepts of somewhat neutrosophic δ-continuous functions, somewhat neutrosophic δ-open functions between neutrosophic topological spaces are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are studied. The concepts of neutrosophic δ-resolvable spaces and neutrosophic δ-irresolvable spaces are also introduced and studied in this paper. These functions can be extended to a somewhat neutrosophic δ-irresolute continuous functions in neutrosophic topological spaces.
Neutrosophic open set , Neutrosophic regular open set , Neutrosophic &delta , -open set , Neutrosophic &delta , -resolvable space , Neutrosophic &delta , -irresolvable space , somewhat Neutrosophic continuous function , somewhat Neutrosophic open function
[1] R.K. Al-Hamido, “A New Approach Of Neutrosophic Topological space”, International Journal of Neutrosophic Science, Vol 7, pp 55-61, 2020.
[2] I. Arokiarani, R. Dhavaseelan, S. Jafari, and M. Parimala, “On some new notions and functions in neutrosophic topological space”, Neutrosophic Sets and Systems, Vol 16, pp 16-19, 2017.
[3] K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Syst., Vol 20, pp 87-96, 1986.
[4] C.L. Chang, “Fuzzy topological space”, J. Math. Anal. Appl., Vol 24, pp 182-190, 1968.
[5] D. Coker, “An introduction to intuitionistic fuzzy topological spaces”, Fuzzy sets and syst., Vol 88, pp 81-89, 1997.
[6] K.R. Gentry and H.B. Hoyle III, “Somewhat continuous functions”, Czech. Math. J., Vol 21 (96), pp 5-12, 1971.
[7] E. Hewitt, “A problem in set theoretic topology”, Duke Math. J., Vol 10, pp 309-333, 1943.
[8] P. Iswarya, and K. Bageerathi, “A Study on Neutrosophic Frontier and Neutrosophic Semi-frontier in Neutrosophic Topological Spaces”, Neutrosophic Sets and Systems, Vol 16, pp 6-15, 2017.
[9] S. Krishna Prabha, Said Broumi, and Selc¸uk Topal, “A Novel Routing Network Algorithm via Netrosophic Fuzzy Set Approach”, International Journal of Neutrosophic Science, Vol 13, pp 9-22, 2021.
[10] M. Parimala, M. Karthika, and F. Smarandache, “A Review of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces and Neutrosophic Soft Topological Spaces”, International Journal of Neutrosophic Science, Vol 10, pp 96-104, 2020.
[11] A.A. Salama, and F. Smarandache, “Neutrosophic crisp set theory”, Educational Publisher, Columbus, Ohio, USA, 2015.
[12] A.A. Salama, and S.A. Alblowi, “Neutrosophic set and neutrosophic topological spaces”, IOSR Journal of Mathematics, Vol 3, pp 31-35, 2012.
[13] A.A. Salama, F. Smarandache, and S.A. Alblowi, “Characteristic function of neutrosophic set”, Neutrosophic Sets and Systems, Vol 3, pp 14-17, 2014.
[14] A.A. Salama, F. Smarandache, and V. Kromov, “Neutrosophic closed set and neutrosophic continuous functions”, Neutrosophic Sets and Systems, Vol 4, pp 4-8, 2014. ‘
[15] A.A. Salama, H. ElGhawalby, and A.M. Nasr, “Star Neutrosophic Fuzzy Topological Space”, International Journal of Neutrosophic Science, Vol 10, pp 77-82, 2019.
[16] F. Smarandache, “A Unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability”, American Research Press, Rehoboth, NM, 1999.
[17] F. Smarandache, “Neutrosophy and neutrosophic logic”, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, NM 87301, USA, 2002.
[18] S. Saha, “Fuzzy δ-continuous maps”, J. Math. Anal. Appl., Vol 126, pp 130-142, 1987.
[19] A. Vadivel and C. John Sundar, “Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps”, International Journal of Neutrosophic Science (IJNS), Vol 13 (2), pp 66-74, 2021.
[20] A. Vadivel and C. John Sundar, “New Operators Using Neutrosophic δ-Open Set”, Journal of Neutrosophic and Fuzzy Systems, Vol 1 (2), pp 61-70, 2021.
[21] A. Vadivel and C. John Sundar, ”Somewhat neutrosophic δ-irresolute continuous mappings in neutrosophic topological spaces”, TWMS Journal of Applied and Engineering Mathematics, Vol 13 (2), pp 773-781, 2023.
[22] A. Vadivel, M. Seenivasan, and C. John Sundar, “An Introduction to δ-open sets in a Neutrosophic Topological Spaces”, Journal of Physics: Conference Series, 1724, 012011, 2021.
[23] A. Vadivel, P. Thangaraja and C. John Sundar, “Neutrosophic e-continuous maps and neutrosophic eirresolute maps”, Turkish Journal of Computer and Mathematics Education, Vol 12 (1S), pp 369-375, 2021.
[24] A. Vadivel, P. Thangaraja and C. John Sundar, “Neutrosophic e-Open Maps, Neutrosophic e-Closed Maps and Neutrosophic e-Homeomorphisms in Neutrosophic Topological Spaces”, AIP Conference Proceedings, 2364, 020016, 2021.
[25] A. Vadivel, P. Thangaraja and C. John Sundar, ”Some Spaces in Neutrosophic e-Open Sets”, Algebra, Analysis, and Associated Topics, Trends in Mathematics, pp 213-25, 2022.
[26] L.A. Zadeh, “Fuzzy sets”, Inform. Control, Vol 8, pp 338-353, 1965.
