Homeomorphisms via $\delta$-open Sets in $n$-Cylindrical Neutrosophic Topological Spaces
DOI:
https://doi.org/10.5269/bspm.83493Abstract
In this article, we introduce the novel notions of $n$-$CyN\delta$ homeomorphisms, $n$-$CyN\delta$ $C$ homeomorphisms, and $n$-$CyN\delta T_{\frac{1}{2}}$-spaces within the framework of $n$-Cylindrical neutrosophic topological spaces. These concepts extend classical homeomorphisms and separation axioms to the neutrosophic setting, incorporating degrees of positive, negative, and neutral membership. We systematically develop and examine key properties and structural features of these notions, establishing several theorems and results that provide deeper insights into their behavior and potential applications in neutrosophic topology.
References
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\bibitem{Ve2017} Y. Veereswari, {\it An introduction to fuzzy neutrosophic topological spaces}, International journal of mathematical archive, 8(3), (2017), 1-6.
\bibitem{Za1965} L. A. Zadeh, {\it Fuzzy sets}, Information and control, 8, (1965), 338-353.
\bibitem{Ana2026} S. Anandhi, R. Vijayalakshmi, and K. Shantha lakshmi, {\it Continuous and Irresolute Maps via $M$-Open Sets in $n$-Cylindrical Neutrosophic Topological Spaces}, AIP Conference Proceeding, (Accepted).
\bibitem{A2026} S. Anandhi, R. Vijayalakshmi, and K. Shantha lakshmi, {\it Contra Continuous and Irresolute Maps Via $M$-Open Sets in $n$-Cylindrical Neutrosophic Topological Spaces}, Neutrosophic Sets and Systems, Vol. 98, (2026), 105-122.
\bibitem{Ar2017} I. Arokiarani, R. Dhavaseelan, S. Jafari \& M. Parimala, {\it On some new notions and functions in neutrosophic topological spaces}, Neutrosophic sets and systems, 16(1), (2017), 16-19.
\bibitem{At1986} K. Atanassov, {\it Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, 20, (1986), 87-96.
\bibitem{Ch1968} C. L. Chang, {\it Fuzzy topological spaces}, J. Math. Anal. Appl., 24, (1968), 182-190.
\bibitem{Co1997} D. Coker, {\it An introduction to intuitionistic fuzzy topological spaces}, Fuzzy sets and systems, 88, (1997), 81-89.
% \bibitem{De1972} A. De Luca, S. Termini, {\it A definition of a non-probabilistic entropy in the setting of fuzzy sets theory}, Information \& Control, 20, (1972), 301-312.
\bibitem{El2011} A. I. El-Maghrabi and M. A. Al-Juhani, {\it $M-$ open sets in topological spacec}, Pioneer J. Math. Sci., 4(2), (2011), 213-230.
\bibitem{Je2005} J. K. Jun, Y. B, \& J. H. Park, {\it Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity}, International journal of mathematics and mathematical science, 19, (2005), 3091-3101.
\bibitem{ka} V. Kalaiyarasan, S. Tamilselvan, A. Vadivel and C. John Sundar, {\it Normal spaces associated with fuzzy nano
$ð‘€$-open sets and its application}, Journal of Mathematics and Computer Science, {\bf 29} (2) (2023), 156-166.
\bibitem{pa} A. Padma, M. Saraswathi, A. Vadivel and G. Saravanakumar, {\it New Notions of Nano $ M $-open Sets}, Malaya Journal of Matematik, \textbf{S} (1) (2019), 656-660.
\bibitem{Sa2012} A. A. Salama, \&S. A. Alblowi, {\it Neutrosophic set and neutrosophic topological spaces}, IOSR journal of mathematics (iosr-jm), 3(4), (2012), 31-35.
\bibitem{Sa2022} R. Saranya Kumari, S. Kalayathankal, M. George, \& F. Smarandache, {\it $n$-Cylindrical Fuzzy Neutrosophic Sets}, International journal of neutrosophic science, 18(4), (2022), 355-374.
\bibitem{Sa2023} R. Saranya Kumari, S. Kalayathankal, M. George, \& F. Smarandache, {\it On some Related Concept of $n$-Cylindrical Fuzzy Neutrosophic Topological Spaces}, Journal of fuzzy extension and applications, Vol. 4, No.1, (2023), 40-51.
\bibitem{Sar2023} R. Saranya Kumari, S. Kalayathankal, M. George, \& F. Smarandache, {\it $n$-Cylindrical Fuzzy Neutrosophic Topological Spaces}, Journal of fuzzy extension and applications, Vol. 4, No.2, (2023), 141-147.
%\bibitem{Sara2023} R. Saranya Kumari, S. Kalayathankal, M. George, \& F. Smarandache, {\it Application of $n$-Cylindrical Fuzzy Neutrosophic Sets in Education Using Neutrosophic Similarity Index and Neutrosophic Score Ratio}, Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education, (2023), 68-88
%\bibitem{Sa2024} R. Saranya Kumari, S. Kalayathankal, M. George, \& F. Smarandache, {\it An Entropy Measure for $n$-Cylindrical Fuzzy Neutrosophic Sets}, Neutrosophic Optimization and Intelligent Systems, 3 (2024), 23-31.
\bibitem{Sma2001} F. Smarandache, {\it A unifying field in logics: neutrosophic logic, neutrosophic set, neutrosophic probability and satistics}, (2001).
\bibitem{Sm2001} F. Smarandache, {\it Proceeding of the first international conference on neutrosophy, neutrosophy logic, neutrosophic set, neutrosophic probability and satistics}, University of New Mexico-Gallup, (2001).
\bibitem{su} S. Suguna, S. Tamilselvan and J. Sathiyaraj, {\it $n$-Cylindrical Neutrosophic $\delta \beta $-open Sets}, Advances in Nonlinear Inequalities, {\bf 28} (3s), 2025, 677-688.
\bibitem{su1} S. Suguna, S. Tamilselvan and J. Sathiyaraj, {\it Continuous and irresolute maps Via $\delta \beta $-open sets in $n$-Cylindrical neutrosophic topological spaces}, Communications on Applied Nonlinear Analysis, {\bf 32} (3s), 2025, 921-933.
\bibitem{th} R. Thangammal, M. Saraswathi, A. Vadivel and C. John Sundar, {\it Fuzzy nano $Z$-open sets in fuzzy nano
topological spaces}, Journal of Linear and Topological Algebra, {\bf 11} (01) (2022), 27-38.
\bibitem{th1} R. Thangammal, M. Saraswathi, A. Vadivel, Samad Noeiaghdam, C. John Sundar, V. Govindan, Aiyared
Iampan, {\it Fuzzy nano $Z$-locally closed sets, extremally disconnected spaces, normal spaces, and their application}, Advances in Fuzzy Systems, (2022), 3364170.
\bibitem{va1} A. Vadivel, C. John Sundar, K. Kirubadevi and S. Tamilselvan, {\it More on Neutrosophic Nano Open Sets},
International Journal of Neutrosophic Science (IJNS), {\bf 18} (4) (2022), 204-222.
\bibitem{va2} A. Vadivel, C. John Sundar, K. Saraswathi and S. Tamilselvan, {\it Neutrosophic Nano $M$-Open Sets},
International Journal of Neutrosophic Science, {\bf 19} (1) (2022), 132-147.
\bibitem{Ve2017} Y. Veereswari, {\it An introduction to fuzzy neutrosophic topological spaces}, International journal of mathematical archive, 8(3), (2017), 1-6.
\bibitem{Za1965} L. A. Zadeh, {\it Fuzzy sets}, Information and control, 8, (1965), 338-353.
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2026-06-09
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