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.