The Role of Complete Parts in Topological Polygroups

Article Sidebar

PDF
Cite as:
M. Salehi Shadkami, M.R. Ahmadi Zand, B. Davvaz, The Role of Complete Parts in Topological Polygroups, Int. J. Anal. Appl., 11 (1) (2016), 54-60.

Main Article Content

M. Salehi Shadkami, M.R. Ahmadi Zand, B. Davvaz

Abstract

A topological polygroup is a polygroup P together with a topology on P such that the polygroup's binary hyperoperation and the polygroup's inverse function are continuous with respect to the topology. In this paper, we present some facts about complete parts in polygroups and we use these facts to obtain some new results in topological polygroups. We define the concept of cp-resolvable topological polygroups. A non-empty subset X of a topological polygroup is called cp-resolvable if there exist disjoint dense subsets A and B such that at least one of them is a complete part. Then, we investigate a few properties of cp-resolvable topological polygroups.

Article Details

References

  1. H. Aghabozorgi, B. Davvaz, M. Jafarpour, Solvable polygroups and derived subpolygroups, Comm. Algebra 41 (2013), 3098-3107.
  2. R. Ameri, Topological (transposition) hypergroups, Ital. J. Pure Appl. Math. 13 (2003), 171-176.
  3. S.D. Comer, Polygroups derived from cogroups, J. Algebra 89 (1984), 397-405.
  4. S.D. Comer, Extension of polygroups by polygroups and their representations using colour schemes, Lecture Notes in Meth. 1004, Universal Algebra and Lattice Theory, 1982, 91-103.
  5. P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.
  6. B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
  7. R. Engelking, General Topology. PWN-Polish Scientific Publishers, Warsaw, 1997.
  8. D. Heidari, B. Davvaz, S.M.S. Modarres, Topological hypergroups in the sense of Marty, Comm. Algebra 42 (2014), 4712-4721.
  9. D. Heidari, B. Davvaz, S.M.S. Modarres, Topological polygroups, Bull. Malays. Math. Sci. Soc., 39 (2016), 707-721.
  10. S. Hoskova-Mayerova, Topological hypergroupoids, Comput. Math. Appl. 64 (2012), 2845-2849.
  11. M. Jafarpour, H. Aghabozorgi, B. Davvaz, On nilpotent and solvable polygroups, Bull. Iranian Math. Soc. 39 (2013), 487-499.
  12. M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pures Appl. 49(1970), 155-192.
  13. F. Marty, Sur une généralization de la notion de groupe, 8iem, Congress Math. Scandinaves, Stockholm, 1934, 45-49.
  14. M. Salehi Shadkami, M. R. Ahmadi Zand and B. Davvaz, Left big subsets of topological polygroups, Filomat, in press.
  15. Y. Sureau, Contribution à la théorie des hypergroupes et hypergroupes opérant transitivement sur un ensemble, Doctoral Thesis, 1980.