Transitivity of The delta^n-Relation in Hypergroups - Saeed Mirvakili; Peyman Ghiasvand (Journal of the Indonesian Mathematical Society, 2018)
The $δ^n$-relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of$δ^{n}$-heart of a hypergroup and we determine necessary andsufficient conditions for the relation $δ^{n}$ to betransitive. Moreover, we determine a family $P_{σ}(H)$ ofsubsets of a hypergroup $H$ and we give sufficient conditionssuch that the geometric space $(H, P_{σ}(H))$ is stronglytransitive and the relation $δ^n$ is transitive.