Soft Topological Space in Virtue of Semi* Open Sets

Year 2020, Volume: 3 Issue: 4, 160 - 166, 23.12.2020

Gnanachandra Prabu , M.lellis Thıvagar , Muneesh Kumar Arumugam

https://doi.org/10.32323/ujma.707355

Abstract

The ultimate purpose of this research article is to originate and examine some new kind of open sets in soft topological spaces such as soft semi* - open and soft semi* - closed sets using generalized closure operator with illustrating counter examples.

Keywords

Soft semi*-closure, Soft semi*-connected, Soft semi*-compact soft semi*-interior, Soft generalized closure, Soft generalized interior

Supporting Institution

Madurai Kamaraj University

Thanks

My special thanks goes to Professor Dr.M.Lellis Thivagar

References

• [1] A. Kharal, B. Ahamad, Mappings on soft classes, New Math.Nat.Comput.7(3) (2011), 471-481.
• [2] A. Robert, S.Pious Missier, A new class of nearly open Sets, Int. J. Math. Arch., 3(7)(2012), 2575-2582.
• [3] A. Robert, S.Pious Missier, On semi*-closed sets , Asian J. Eng. Maths., 1(4) (2012), 173-176.
• [4] C. Gunduz Aras, S. Bayramov, On the Tietze extension theorem in soft topological spaces, Proc. Inst. Math. Mech., 43 (1) (2017), 105-115.
• [5] D. Molodtsov, Soft set theory-first results, Comp. Math. Appl., 37 (1999), 19-31.
• [6] E. Peyghan, B. Samadi, A. Tayebi, On soft connectedness, arXiv:1202.1668V1 [math.GN], 8 Feb 2012.
• [7] I. Demir, An approach to the concept of soft vietoris topology, Int. J. Anal. Appl., 12 (2016), 198-206.
• [8] I. Demir, O.B. Ozbakir, I. Yıldız, A contribution to the study of soft proximity spaces, Filomat, 31 (2017) 2023 - 2034.
• [9] I. Demir, O. B. Ozbakir, An extension of Lowen’s uniformity to the fuzzy soft sets, Konuralp J. Math., 6 (2018) 321 - 331.
• [10] I. Zorlutuna, M. Akdag, W.K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2) (2012), 171-185.
• [11] K. Kannan Soft generalized closed sets in soft topological spaces, J. Theoret. Appl. Tech., 37 (2012), 17-21.
• [12] M. Shabir, M. Naz, On Soft topological spaces, Comp. Math. Appl., 61(2011), 1786-1799.
• [13] M.E. El-Shafei, M. Abo-Elhamayel, T.M. Al-Shami, Two notes on ”On soft Hausdorff spaces”, Ann. of Fuzzy Math. Inform., 16 (3) (2018), 333-336.
• [14] N. Levine, Semi-open sets and Semi- continuity in topological spaces, Amer. Math. Monthly, 70(1) (1963), 36-41.
• [15] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (1970),89–96.
• [16] P.K.Maji, R.Biswas, R.Roy Soft set theory, Computer and Mathematics with Applications 45(2003) 555-562.
• [17] S.Hussain, B.Ahmed,Some Properties of Soft Topological Spaces, Comput. Math. Appl., 62 (2011), 4048-4067.
• [18] S. Pious Missier, A. Robert On semi*-open sets , International Journal of Mathematics and soft computing, 2(2)(2012)95-105.
• [19] S.M.Khalil, M.Ulrazaq, S.Abdul-Ghani, A.F. Al-Musawi, s-Algebra and s-Baire in Fuzzy Soft Setting, Advances in Fuzzy Systems , Volume 2018, Article ID 5731682, 10 pages. 7(3),(2011),471-481.
• [20] S.M.Khalil, Decision making using algebraic operations on soft effect matrix as new category of similarity measures and study their application in medical diagnosis problems , Journal of Intelligent and Fuzzy Systems, 37(2019) ,1865-1877.
• [21] W. Dunham, A New Closure Operator for Non-T1 Topologies, Kyungpook Math. J. 22 (1982), 55–60.
• [22] W.K.Min, A Note on Soft Topological Spaces, Comput. Math. Appl., 62(2011),3524-3528.