Some basic properties of -hyperstructures

In canonical books on hyperstructures a number of applications of hyperstructure theory and its relations to various areas of mathematics are included. The relations of hyperstructures and ordered sets have been touched upon by Vougiouklis or Corsini. One aspect of this issue was thoroughly studied by Chvalina and Rosenberg. Cristea, Spartalis and others have been exploring other aspects such as generalization of the relations or constructing special cases. In this paper we present a theoretical background for the use of the “Ends lemma” — another construction often used to create hyperstructures from quasi/partially ordered (semi)groups in a number of contexts including the study of differential equations, matrix theory or applications of preference relations in microeconomics.