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International Journal of Neutrosophic Science
Volume 22 , Issue 2, PP: 15-28 , 2023 | Cite this article as | XML | Html |PDF

Title

Pre-separation Axioms in Neutrosophic Topological Spaces

  Sudeep Dey 1 * ,   Gautam Chandra Ray 2

1  Department of Mathematics, Science College, Kokrajhar, Assam, India ; Department of Mathematics, Central Institute of Technology, Kokrajhar, Assam, India
    (sudeep.dey.1976@gmail.com)

2  Department of Mathematics, Central Institute of Technology, Kokrajhar, Assam, India
    (gautomofcit@gmail.com)

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Doi   :   https://doi.org/10.54216/IJNS.220202

Received: March 12, 2023 Revised: June 02, 2023 Accepted: September 02, 2023

Abstract :

In this article, we first establish a few relationships among neutrosophic interior, neutrosophic closure, neutrosophic pre-open sets, and neutrosophic pre-closed sets in single-valued neutrosophic topological spaces. Thereafter, we defined neutrosophic pre-  space, neutrosophic pre-  space, and neutrosophic pre-  space based on single-valued neutrosophic topological spaces and studied a few properties and relationships among them. We try to establish some relationships between existing neutrosophic separation axioms and newly defined neutrosophic pre-separation axioms. Finally, we study some hereditary properties of pre-separation axioms. Apart from these, we also explore some results implementing neutrosophic pre-open function, neutrosophic pre-continuous function, neutrosophic pre-irresolute function and neutrosophic pre -function based on our defined definitions.

 

Keywords :

Neutrosophic subspace ; Neutrosophic pre- space ; Neutrosophic pre- space ; Neutrosophic pre-  space ; Neutrosophic pre-open set ; Neutrosophic pre-closed set ; Neutrosophic pre-open function ; Neutrosophic pre-continuous function ; Neutrosophic pre-irresolute function ; Neutrosophic pre -continuous function.  

References :

[1] Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.

[2] Arokiarani, I.; Dhavaseelan, R.; Jafari, S.; Parimala, M. (2017). On Some New Notions and Functions in Neutrosophic Topological Space. Neutrosophic Sets and Systems, 16, 16-19.

[3] Alblowi, S. A. and Salma, A. A.; Eisa, M. (2014). New concepts of neutrosophic sets. Int. J. of Math and Comp. Appl. Research, 4(1), 59-66.

[4] Aҫikgӧz, A.and  Esenbel, F. (2020). An Approach to pre-separation axioms in neutrosophic soft topological spaces, Commun.Fac.Sci.Univ.Ank.Ser. A1 Math. Stat., 69(2), 1389-1404.

[5] Aҫikgӧz, A. and Esenbel, F. (2021). A look on separation axioms in neutrosophic topological spaces. AIP Conference Proceedings, Turkey, 17-21 June, 2020, AIP Publishing, https://doi.org/10.1063/5.0042370.

[6] Coker, D. (1997). An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 81-89.

[7] Dey. S. and Ray, G. C. Covering properties in Neutrosophic Topological Spaces. Neutrosophic Sets and Systems, 51, 525-537.

[8] Dey. S and Ray, G. C. (2023). Separation Axioms in Neutrosophic Topological Spaces. Neutrosophic Systems withApplications, 2, 38-54. DOI: https://doi.org/10.5281/zenodo.8195851

[9] Dey. S. and Ray, G. C. (2023). Neutrosophic Pre-compactness. International Journal of Neutrosophic Science, 21(1), 105-120.

[10] Karatas, S., and Kuru, C. (2016). Neutrosophic Topology. Neutrosophic Sets and Systems, 13(1), 90-95.

[11] Rao, V. V. and Rao, Y. S. (2017). Neutrosophic Pre-open Sets and Pre-closed Sets in Neutrosophic Topology, International Journal of ChemTech Research, 10(10), 449-458.

[12] Ray, G. C. and Dey, S. (2021). Neutrosophic point and its neighbourhood structure. Neutrosophic Sets and Systems, 43, 156-168.

[13] Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, Rehoboth, NM.

[14] 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 .

[15] Smarandache,F. (2005). Neutrosophic set - a generalization of the intuitionistic fuzzy set. International Journal of Pure and Applied Mathematics, 24(3), 287-297.

[16] Salama, A.A., and Alblowi, S. (2012). Neutrosophic set and Neutrosophic Topological Spaces. IOSR Journal of Mathematics, 3(4), 31-35.

[17] Salama, A. A., Smarandache, F. and Kroumov, V. (2014). Closed sets and Neutrosophic Continuous Functions, Neutrosophic Sets and Systems, 4, 4-8.

[18] Ṣenyurt, S., and Kaya, G. (2017). On Neutrosophic Continuity. Ordu University Journal of Science and Technology, 7(2), 330-339.

[19] Sudha, V., Vadivel, A. and Tamilselvan, S.; (2021). Separation Axioms in Nnc Topological Spaces via Nnc e-open Sets, Journal of Physics: Conference Series 1724 012014, ICRTAMS 2020, India, 26-27 September, IOP Publishing, DOI:10.1088/1742-6596/1724/1/012014.

[20] Suresh, R. and Palaniammal, S. (2020). NS (WG) separation axioms in Neutrosophic topological spaces. Journal of  Physics: Conference Series 1597 012048, International Conference on New Trends in Mathematical Modelling with Applications, India, 29-30 July 2019, IOP Publishing, doi:10.1088/1742-6596/1597/1/012048.

[21] Wang, H. and Smarandache, F.; Zhang, Y.Q. ; Sunderraman, R. (2010). Single valued neutrosophic sets, Multispace Multistruct, 4, 410-413.

[22] Zadeh, L. A. (1965). Fuzzy sets. Inform. and Control, 8, 338-353.

Cite this Article as :
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MLA Sudeep Dey, Gautam Chandra Ray. "Pre-separation Axioms in Neutrosophic Topological Spaces." International Journal of Neutrosophic Science, Vol. 22, No. 2, 2023 ,PP. 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
APA Sudeep Dey, Gautam Chandra Ray. (2023). Pre-separation Axioms in Neutrosophic Topological Spaces. Journal of International Journal of Neutrosophic Science, 22 ( 2 ), 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
Chicago Sudeep Dey, Gautam Chandra Ray. "Pre-separation Axioms in Neutrosophic Topological Spaces." Journal of International Journal of Neutrosophic Science, 22 no. 2 (2023): 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
Harvard Sudeep Dey, Gautam Chandra Ray. (2023). Pre-separation Axioms in Neutrosophic Topological Spaces. Journal of International Journal of Neutrosophic Science, 22 ( 2 ), 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
Vancouver Sudeep Dey, Gautam Chandra Ray. Pre-separation Axioms in Neutrosophic Topological Spaces. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 2 ): 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
IEEE Sudeep Dey, Gautam Chandra Ray, Pre-separation Axioms in Neutrosophic Topological Spaces, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 2 , (2023) : 15-28 (Doi   :  https://doi.org/10.54216/IJNS.220202)
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