Quasi-Order Hypergroups and T-Hypergroups

Abstract

Quasi-order hypergroups were introduced by J. Chvalina in 90s of the last century. They form a subclass of the class of all hypergroups, i.e. structures with one associative hyperoperation fulfilling the reproduction axiom. In this paper a theorem which allows an easy description of all quasi-order hyper- groups is mentioned and some results concerning the relation of quasi-order and upper quasi-order hypergroups are given. Furthermore the transformation hypergroups acting on tolerance spaces are defined and an example of them is given

Keywords

• Quasi-order hypergroup
• order hypergroup
• tolerance relation
• transformation semihypergroup
• transformation hypergroup