Analysis on Semihypergroups

  • Author / Creator
    Bandyopadhyay, Choiti
  • The concepts of semihypergroups and hypergroups were first introduced by C. Dunkl, I. Jewett and R. Spector independently around the year 1972. Till then, a variety of research has been carried out on different areas of hypergroups. However, no extensive study is found so far on the more general category of semihypergroups, which serves as building blocks of the hypergroup theory. In this thesis, we initiate a systematic study of semihypergroups. We introduce and study several natural algebraic and analytic stuctures on semihypergroups, which are well-known in the case of topological semigroups and groups. In particular, we study semihypergroup actions, almost periodic and weakly almost periodic function spaces, ideals, homomorphisms and free structures in the category of semihypergroups, and finally investigate where the theory deviates from the classical theory of (topological) semigroups.

  • Subjects / Keywords
  • Graduation date
    Spring 2018
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
  • Examining committee members and their departments
    • Dr. Feng Dai, Department of Mathematical and Statistical Sciences
    • Dr. Michael Li, Department of Mathematical and Statistical Sciences
    • Dr. Tahir Choulli, Department of Mathematical and Statistical Sciences
    • Dr. Vladimir Troitsky, Department of Mathematical and Statistical Sciences
    • Dr. Fereidoun Ghahramani, Department of Mathematics, University of Manitoba