Hypergroupoids and fundamental relation

In this work we study hypergroupoids whose \u3b2-relation is transitive, by using the fundamental relations \u3b2, \u3b2*, \u3b4 and \u3b4*. We take several examples, finding the necessary and sufficient conditions such that a quasi-hypergroup has \u3b2*=\u3b2=\u3b4=\u3b4* (i.e. it is of kind T_1). We shall find that c-completable quasi-hypergroups with identity are of kind T_1 and this gives that every H_v-group with identity is of kind T_1