Gnanachandra PRABU, M.lellis THIVAGAR, Muneesh Kumar ARUMUGAM

Soft Topological Space in Virtue of Semi* Open Sets

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,

PDF

___

[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.