Year 2020,
Volume: 3 Issue: 4, 160 - 166, 23.12.2020
Gnanachandra Prabu
M.lellis Thıvagar
Muneesh Kumar Arumugam
References
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- [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.
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- [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.
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
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.
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.