Hausdorff Space Based on $KM$-Single Valued Neutrosophic Space

Document Type : Research Paper

Author

Department of Mathematics, University of Payame Noor, Tehran, Iran

Abstract

This paper introduces a novel concept of $KM$-single valued neutrosophic Hausdorff space and $KM$-single valued neutrosophic manifold space. This study generalizes the concept of $KM$-single valued neutrosophic manifold space to union and product of $KM$-single valued neutrosophic manifold space and in this regard investigates some product of $KM$-single valued neutrosophic manifold spaces. Indeed, this study analyses the notation of $KM$-single valued neutrosophic manifold based on a valued-level subset.

Keywords


[1] M. Ferraro, D. Foster, Di erentiation of Fuzzy Continuous Mappings on Fuzzy Topological Vector Spaces, Journal of Mathematical Analysis and Applications, 121 (1987),589-601.
[2] V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems, 170 (2011), 95{111.
[3] M. J. Lee, Introduction to Smooth Manifolds, Springer Science, New York, 2003.
[4] M. Hirsch, Di erential Topology, Springer, New York, 6th edition, 1997.
[5] K. Katsara and D. B. Liu, Fuzzy vector space and fuzzy topological vector spaces, J. Math. Anal. Appl., 58 (1977), 135-146.
[6] O. Kaleva and S. Seikkala, On Fuzzy Metric Spaces, Fuzzy Sets and Systems, 12 (1984), 215{229.
[7] R. Lowen, Fuzzy topological space and fuzzy compactness, J. Math. Anal. Appl., 56 (1976), 621-633.
[8] A. Mehmmod, , F. nadeem, M. Mudasser, U. Kalsoom, S. Jabeen, SOFT  -Structures In BI-Polar Soft Topological Spaces, 9(1) (2020), 1{22.
[9] J. Martina Jency, I. Arockiarani, Hausdor  Extensions in Single Valued Neutrosophic S-Centered Systems, Published in Florentin Smarandache & Surapati Pramanik (Editors):New Trends in Neutrosophic Theory and Applications, Pons Editions, Brussels, Belgium,EU, ISBN 978-1-59973-498-9, (2016), 327-344.
[10] B. M. Pu and Y. M. Liu, Fuzzy topology I: Neighborhood structure of a fuzzy point and Moore smith convergence, J. Math. Anal. Appl., 76(1980), 571-599
[11] G. Rano and T. Bag, Fuzzy Normed Linear Spaces, International Journal Of Mathematics and Scienti c Computing, 2 (2012), 16-19.
[12] R. Saadati and M. Vaezpour, Some Results On Fuzzy Banach Spaces, J. Appl. Math.and Computing, 17(2005), 475-484.
[13] I. R. Sumathi, C. Antony Crispin Sweety, New approach on di erential equation via trapezoidal neutrosophic number, Complex & Intelligent Systems, (2019).
[14] S. Sahin, A. Kargn and M. Yucel,Hausdor  Measures on Generalized Set Valued Neutrosophic Quadruple Numbers and Decision Making Applications for Adequacy of Online Education, Neutrosophic Sets and Systems, 40 (2021), 86{116.
[15] A. Talabeigi, An approach to change the topology of a topological space with the help of its closed sets in the presence of grills, 10(2) (2021), 9-19.
[16] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338{353.