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

  • Free product
  • Hypergroups
  • Ideal
  • Semihypergroup
  • Measure
  • Action
  • Almost periodic function
  • Homomorphism

• Graduation date

  Spring 2018

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3WD3QG81

• 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.