Soft semi-topological polygroups

Year 2022, Volume: 71 Issue: 3, 689 - 709, 30.09.2022

Rasoul Mousarezaei , B. Davvaz

https://doi.org/10.31801/cfsuasmas.997442

Abstract

By removing the condition that the inverse function is continuous in soft topological polygroups, we will have less constraint to obtain the results. We offer different definitions for soft topological polygroups and eliminate the inverse function continuity condition to have more freedom of action.

Keywords

Soft sets, polygroups, soft polygroups, topological polygroup, soft topological polygroups, complete part, closure sets, semi-topological polygroups, soft semi-topological semigroups

References

• Aktas, H., Cagman, N., Soft sets and soft groups, Information Sciences, 77(13) (2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
• Aygunoglu, A., Aygun, H., Some notes on soft topological spaces, Neural Comput. & Applic., 21(1) (2012), 113-119. https://doi.org/10.1007/s00521-011-0722-3
• Babitha, K.V., Sunil, J.J., Soft set relations and functions, Comput. Math. Appl., 60(7) (2010), 1840-1849. https://doi.org/10.1016/j.camwa.2010.07.014
• Cagman, N., Karatas, S., Enginoglu, S., Soft topology, Comput. Math. Appl., 62(1) (2011), 351-358. https://doi.org/10.1016/j.camwa.2011.05.016
• Corsini, P., Prolegomena of Hypergroup Theory, Aviani Editore, Tricesimo, Italy, 1993.
• Comer, S.D., Extension of polygroups by polygroups and their representations using color schemes, Universal algebra and lattice theory (Puebla, 1982), 91–103, Lecture Notes in Math., 1004, Springer, Berlin, 1983. https://doi.org/10.1007/BFb0063431
• Davvaz, B., Polygroup Theory and Related Systems,World Scientific Publishing Co. Pte.Ltd., Hackensack, NJ, 2013. https://doi.org/10.1142/8593
• Feng, F., Li, Y.M., Soft subsets and soft product operations, Information Sciences, 232 (2013), 44-57. https://doi.org/10.1016/j.ins.2013.01.001
• Heidari, D., Davvaz, B., Modarres, S.M.S., Topological polygroups, Bull. Malays. Math. Sci. Soc., 39 (2016), 707-721. https://doi.org/10.1007/s40840-015-0136-y
• Hewitt, E., Ross, K.A., Abstract Harmonic Analysis, vol. 1, Springer Verlag, Berlin, 1963.
• Hida, T., Soft topological group, Annals Fuzzy Mathematics and Informatics, 8(6) (2014), 1001-1025.
• Hoskova-Mayerova, S., Topological hypergroupoids, Comput. Math. Appl., 64(9) (2012), 2845-2849. https://doi.org/10.1016/j.camwa.2012.04.017
• Kharal, A., Ahmad, B., Mappings on soft classes, New Math Nat. Comput., 7(3) (2011), 471-481. https://doi.org/10.1142/S1793005711002025
• Koskas, M., Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pures Appl., 49(9) (1970), 155-192.
• Maji, P.K., Biswas, R., Roy, A.R., Soft set theory, Comput. Math. Appl. 45(4-5) (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
• Marty, F., Sur une g´en´eralization de la notion de groupe, 8iem, Congress Math. Scandinaves, Stockholm, (1934) 45-49.
• Molodtsov, D., Soft set Theory-First Results, Comput. Math. Appl., 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
• Mousarezaei, R., Davvaz, B., On soft topological polygroups and their examples, International Journal of Fuzzy Logic and Intelligent Systems, 21(1) (2021), 29-37. http://doi.org/10.5391/IJFIS.2021.21.1.29
• Nazmul, S., Samanta, S.K., Group soft topology, J. Fuzzy Math., 22(2) (2014), 435-450.
• Nazmul, S., Samanta, S.K., Neighbourhood properties of soft topological spaces, Annals Fuzzy Mathematics and Informatics, 6(1) (2013), 1-15.
• Nazmul, S., Samanta, S.K., Soft topological soft groups, Mathematical Sciences, 6 (2012) 1-10. https://doi.org/10.1186/2251-7456-6-66
• Oguz, G., A new view on topological polygroups, Turkish Journal of Science, 5(2) (2020), 110-117.
• Oguz, G., Idealistic soft topological hyperrings, Scientific Inquiry and Review, 4(3) (2020), 61-70.
• Oguz, G., On soft topological hypergroups, Journal of Hyperstructures, 9(2) (2021), 81-95.
• Oguz, G., Davvaz, B., Soft topological hyperstructure, Journal of Intelligent and Fuzzy Systems, 40(5) (2021), 8755-8764. https://doi.org/10.3233/JIFS-200242
• Shabir, M., Naz, M., On soft topological spaces, Comput. Math. Appl., 61(7) (2011), 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006
• Shah, T., Shaheen, S., Soft topological groups and rings, Annals Fuzzy Mathematics and Informatics, 7(5) (2014), 725-743.