A New View on Topological Polygroups

Year 2020, Volume: 5 Issue: 2, 110 - 117, 31.10.2020

Gülay Oğuz

Abstract

Soft set theory, defined by Molodtsov as a novel mathematical tool modeling uncertainty, has been combined with many different discipline fields. In this article, the concept of soft topological polygroups is proposed by examining polygroups, a special class of hypergroups, with a soft topological approach. Also, several results have been obtained by establishing important characterizations related to this concept. Inlast, bypresentingthe definitionof softtopologicalsubpolygroups,someoftheir properties are examined.

Keywords

Soft set , soft topological group , topological polygroup , soft topological polygroup

References

• Molodtsov, D. A.(1999). Soft set theory-First results. Comput. Math. Appl., 37(4-5), 19-31.
• Marty,F.(1934). SuruneGeneralisation dela NotiondeGroupe.8thCongress MathematiciensScandinaves,Stockholm, pp.45–49.
• Aktas, H., Cagman, N.(2007). Soft sets and soft groups. Inform. Sci., 77(13), 2726–2735.
• Maji, P. K., Biswas, R., Roy, A. R.(2003). Soft set theory. Comput. Math. Appl., 45(4-5), 555–562.
• Kazanci, O., Yilmaz, S., Yamak, S.(2010). Soft sets and soft BCH-algebras. Hacettepe J. Math. Stat., 39, 205–217.
• Shabir, M., Naz, M.(2011). On soft topological spaces. Comput. Math. Appl., 61(7), 1786-1799.
• Oguz, G., Gursoy, M.H., Icen, I.(2019). On soft topological categories. Hacet. J. Math. Stat., 48(6), 1675–1681.
• Jun, Y.B. (2008). Soft BCK/BCI-algebras. Comput. Math. Appl., 56, 1408–1413.
• Oguz, G., Icen, I., Gursoy, M.H.(2019). Actions of soft groups.Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1), 1163–1174.
• Corsini, P., Leoreanu, V.(2003). Applications of Hyperstructure Theory. in: Advances in Math-ematics, vol. 5, Kluwer Academic Publishers Boston, Mass.
• Aygunoglu, A., Aygun, A.(2012). Some notes on soft topological spaces. Neural Comput. Appl., 22(1), 113–119.
• Yamak, S., Kazanci, O., Davvaz, B.(2011). Soft hyperstructure. Comput. Math. with Appl., 62(2), 797–803.
• Leoreanu Fotea, V., Corsini, P.(2010) Soft hypergroups. Critical Review. A publication of Society for Mathematics of Uncertainty, Creighton University - USA, July , vol. IV, 81–97.
• Wanga, J., Yin, M., Gua, W.(2011) Soft polygroups. Comp. Math. Appl., 62, 3529–3537.
• Davvaz, B.(2000) On polygroups and permutation polygroups. Math. Balkanica (N.S.), 14 (1-2), 41–58.
• Davvaz, B., Poursalavati N. S.(1999). On polygroup hyperrings and representations of polygroups. J. Korean Math. Soc., 36 (6), 1021–1031.
• Ioulidis, S.(1981). Polygroups et certain de leurs properties. Bull. Greek Math. Soc., 22, 95-–104.
• Comer, S.D.(1984). Polygroups derived from cogroups. J. Algebra, 89, 397—405.
• Heidari, D., Davvaz, B., Modarres, S. M. S. (2016). Topological polygroups. B. Malays. Math. Sci. Soc., 39(2), 707–721.