Separation Axioms on Topological \(\Gamma\)-Semihypergroups

Abstract

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 \(\mid H \mid =1.\)