University of GuilanJournal of Algebra and Related Topics2345-39318220201201Relations between G-sets and their associate G^{\hat}-sets7591442210.22124/jart.2020.17806.1232ENN.Rakhsh KhorshidDepartment of Mathematics, University of Hormozgan, Bandar Abbas, IranS.Ostadhadi-DehkordiDepartment of Mathematics, University of Hormozgan, Bandar Abbas, IranJournal Article20200927In this paper, we define and consider $G$-set on<br />$\Gamma$-semihypergroups and we obtain relations between $G$-sets<br />and their associate $\widehat{G}$-sets where $G$ is a<br />$\Gamma$-semihypergroup and $\widehat{G}$ is an associated<br />semihypergroup. Finally, we obtain the relation between direct limit of $\widehat{G}$-sets from the direct limit defined on<br /> $G$-sets.https://jart.guilan.ac.ir/article_4422_2ba69b51a111a29742107433b92aaab6.pdf