Hypergroups Associated with Ternary Relations and the Associated Join Space of the Spherical Geometry
Keywords:Ternary relations, Hypergroups, Join spaces, Spherical Geometry, Associated join space.
AbstractThe paper deals with hypergroupoids obtained from ternary relations.The correspondence between ternary relation and hypergroups, studied by the author, especially in the case when the relation is symmetric and reflexive, is analyzed here in the most general context. A necessary and sufficient condition on a ternary relation R is obtained for the associated hypergroupoid to be a hypergroup or a join space. Extension of a hyperoperation associated with a ternary relation being employed to obtain a associated join space of the spherical geometry.
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