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A New View on Topological Polygroups

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

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.

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

Abstract

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.
There are 19 citations in total.

Details

Primary Language English
Journal Section Volume V Issue II 2020
Authors

Gülay Oğuz

Publication Date October 31, 2020
Published in Issue Year 2020 Volume: 5 Issue: 2

Cite

APA Oğuz, G. (2020). A New View on Topological Polygroups. Turkish Journal of Science, 5(2), 110-117.
AMA Oğuz G. A New View on Topological Polygroups. TJOS. October 2020;5(2):110-117.
Chicago Oğuz, Gülay. “A New View on Topological Polygroups”. Turkish Journal of Science 5, no. 2 (October 2020): 110-17.
EndNote Oğuz G (October 1, 2020) A New View on Topological Polygroups. Turkish Journal of Science 5 2 110–117.
IEEE G. Oğuz, “A New View on Topological Polygroups”, TJOS, vol. 5, no. 2, pp. 110–117, 2020.
ISNAD Oğuz, Gülay. “A New View on Topological Polygroups”. Turkish Journal of Science 5/2 (October 2020), 110-117.
JAMA Oğuz G. A New View on Topological Polygroups. TJOS. 2020;5:110–117.
MLA Oğuz, Gülay. “A New View on Topological Polygroups”. Turkish Journal of Science, vol. 5, no. 2, 2020, pp. 110-7.
Vancouver Oğuz G. A New View on Topological Polygroups. TJOS. 2020;5(2):110-7.