BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES

Abstract

The striking idea of soft sets was frst claimed that by Molodtsov as a new mathematical tool for dealing with uncertainties which is free from the other theories limitations. After the advent of soft set theory, bipolar soft sets as a generalization of soft sets, a new model of uncertain information, were introduced by Shabir and Naz. The main purpose of this paper is to introduce and investigate the structures of bipolar soft continuity, bipolar soft openness, bipolar soft closedness and bipolar soft homeomorphism.

Keywords

• Bipolar soft set
• Bipolar soft topological space
• Bipolar soft continuity

References

1. M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553.
2. T.M. Al-Shami, Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 33(4) (2018), 1341-1356.
3. T.M. Al-Shami, M.E. El-Shafei, Partial belong relation on soft separation axioms and decision-making roblem, two birds with one stone, Soft Computing, 24(7) (2020), 5377-5387.
4. M Aslam, S. Abdullah and K. Ullah, Bipolar fuzzy soft sets and its applications in decision making problem, J. Intell. Fuzzy Systems, 27(2) (2014), 729-742.
5. S. Bayramov and C. Gunduz , Soft locally compact spaces and soft paracompact spaces, Journal of Math. and Sys. Sci. 3, (2013), 122-130.
6. S. Bayramov and C. Gunduz , A new approach to separability and compactness in soft topological spaces, TWMS Journal of Pure and Applied Mathematics, 9(1) (2018), 82-93.
7. A.Fadel, S.C.Dzul-Kii, Bipolar soft topological spaces, European Journal of Pure and Applied Mathematics, 13 (2020), 227-245.
8. A.Fadel, S.C.Dzul-Kii, Bipolar soft functions, AIMS Mathematics, 6(5) (2021), 4428-4446.

9. C. Gunduz Aras and S. Bayramov, On the Tietze extension theorem in soft topological spaces, Proc. of Inst.Math. and Mech., 43(1) (2017), 105-115.
10. C. Gunduz Aras, T.M. Al-Shami, A. Mhemdi, S. Bayramov, Local compactness and para- compactness on soft bipolar topological spaces, J. Intell. Fuzzy Systems, 43 (2022), 6755- 6763.
11. C. G. Aras, A.Sonmez, H.Cakallı, An approach to soft functions, J.Math.Anal., 8 (2017), 129-138.
12. C. G. Aras, C. Metin, A note on bipolar soft continuity, International Conference of Math-ematical Sciences, 2021.
13. H. Posul, C. G. Aras, Servet Kutukcu,Soft A-Metric Spaces, Journal of New Theory, 41 (2022) 70-81.
14. K. Hayat and T. Mahmood, Some applications of bipolar soft set: Characterizations of two isomorphic Hemi-rings via BSI-h-Ideals, British Journal of Mathematics and Computer Sciences, 13 (2015), 1-21.
15. F. Karaaslan and S. Karatas, A new approach to bipolar soft sets and its applications, Discrete Mathematics, Algorithms and Applications, 7(4) (2015), 14 pg.
16. P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562.
17. P. Majumdar, S.K.Samanta, On soft mappings, Comput. Math. Appl., 60 (2010), 2666-2672.
18. D. A. Molodtsov, Soft set theory-rst results, Comput. Math. Appl., 37 (1999), 19-31.
19. T.Y Ozturk, On bipolar soft topological spaces, J. New Theory, 20 (2018), 64-75.
20. T.Y Ozturk, On bipolar soft points, TWMS J. App. and Eng. Math., 10(4) (2020), 877-885.
21. M. Shabir, M. Naz, On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344v1 (2013).
22. M. Naz and M. Shabir, On fuzzy bipolar soft sets, their algebraic structures and applications, J. Intell. Fuzzy Systems, 26(4) (2014), 1645-1656.
23. M. Shabir and A. Bakhtawar, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakarin Journal of Science and Technology, 39(3) (2017), 359-371.