Decomposition of soft continuity via soft locally b-closed set

Abstract

In this paper, we introduce soft locally b-closed sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters and study some of their properties. We investigate their relationships with different types of subsets of soft topological spaces with the help of counterexamples. Also, the concept of soft locally b-continuous functions is presented. Finally, a decomposition of soft continuity is obtained.

Keywords

• Soft set,Soft topological space,Soft locally b-closed set,soft locally b--continuous function

References

1. Akdag M. and Ozkan A., Soft α-open sets and soft α-continuous functions, Abstract and Applied Analysis, http://dx.doi.org/10.1155/2014/891341, 2014.
2. Akdag M. and Ozkan A., Soft b-open sets and soft b-continuous functions, Math. Sci., (2014), 8(124).
3. Akdag M. and Ozkan A., On soft preopen sets and soft pre separation axioms, Gazi University Journal of Science, 27(4), (2014), 1077-1083.
4. Al-Salem S. M., Soft regular generalized b-closed sets in soft topological spaces, Journal of Linear and Topological Algebra, 3(4), (2014), 195-204.
5. Ali M.I., Feng F., Liu X., Min W.K. and Shabir M., On some new operations in soft set theory, Computers and Mathematics with Applications, 57, (2009), 1547-1553.
6. Arockiarani I. and Arokialancy A., Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces, International Journal of Mathematical Archive, 4(2), (2013), 1-7.
7. Aygünoğlu A. and Aygün H., Some notes on soft topological spaces, Neural Computing and Applications, 21(1), (2012), 113-119.
8. Chen B., Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics & Information Sciences, 7(1), (2013), 287-294.

9. Feng F., Jun Y.B. and Zhao X.Z., Soft semirings, Computers and Mathematics with Applications, 56, (2008), 2621-2628.
10. Guzel Ergul Z. and Tozlu N., Decompositions of soft continuity and soft AB-continuity, Annals of Fuzzy Mathematics and Informatics, 14(5), (2017), 463-474.
11. Hussain S. and Ahmad B., Some properties of soft topological spaces, Computers and Mathematics with Applications, 62(11), (2011), 4058-4067.
12. Kandil A., Tantawy O.A.E., El-Sheikh S.A. and Abd El-latif A.M., γ-operation and decompositions of some forms of soft continuity in soft topological spaces, Ann. Fuzzy Math. Inform., 7(2), (2014), 181-196.
13. Kharal A. and Ahmad B., Mappings on soft classes, New Mathematics and Natural Computation, 7(3), (2011), 471-481.
14. Kocaman A.H. and Tozlu N., Soft locally closed sets and decompositions of soft continuity, Annals of Fuzzy Mathematics and Informatics, 11(2), (2016), 173-181.
15. Mahanta J. and Das P.K., On soft topological space via semi-open and semi-closed soft sets, Cornell University Library, arXiv:1203.4133, 2012.
16. Maji P.K., Roy A.R. and Biswas R., An application of soft sets in decision making problem, Computers and Mathematics with Applications, 44, (2002), 1077-1083.
17. Maji P.K., Biswas R. and Roy A.R., Soft set theory, Computers and Mathematics with Applications, 45(4-5), (2003), 555-562.
18. Molodtsov D., Soft set theory-first results, Computers and Mathematics with Applications, 37(4-5), (1999), 19-31.
19. Molodtsov D., Leonov V.Y. and Kovkov D.V., Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 9(1), (2006), 8-39.
20. Shabir M. and Naz M., On soft topological spaces, Computers and Mathematics with Applications, 61(7), (2011), 1786-1799.
21. Tozlu N. and Yüksel Ş., Soft A-sets and soft B-sets in soft topological spaces, Mathematical Sciences & Applications E- Notes, 5(2), (2017), 17-25.
22. Yüksel Ş., Tozlu N. and Güzel Ergül Z., Soft regular generalized closed sets in soft topological spaces, International Journal of Mathematical Analysis, 8(8), (2014), 355-367.
23. Yuksel S., Guzel Ergul Z. and Guven Z., Soft connected spaces, International J. of Pure & Engg. Mathematics, 2(3), (2014), 121-134.
24. Zorlutuna I., Akdağ M., Min W.K. and Atmaca S., Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2), (2012), 171-185.