In this paper, we investigate the concept of topological \(\Gamma\) -semihypergroups as a generalization of topological semihypergroups. Also, we present the new connection between topological \(\Gamma\) -semihypergroups and topological semihypergroups by special equivalence relation. Furthermore, we define and consider \(\Gamma\) -hyperideals and selection function on \(\Gamma\) -semihypergroups. Additionally, we consider separation axioms( \(T_1\) to \(T_4\) ) for topological \(\Gamma\) -semihypergroup and we present a connection between topological \(\Gamma\) -semihypergroups and topological semihypergroups(semigroups). Finally, we prove that topological \(\Gamma\) -semihypergroup H is \(T_i,\) for \(1\le i \le 4\) if and only if \(\mid H \mid =1.\)
