Topological Polygroups

Abstract

This paper deals with certain algebraic systems called polygroups. A polygroup is a completely regular, reversible in itself hypergroup. The concept of topological polygroups is a generalization of the concept of topological groups. In this paper, we present the concept of topological hypergroups and prove some properties. Then, we define the notion of topological polygroups. By considering the relative topology on subpolygroups we prove some properties of them. Finally, the topological isomorphism theorems of topological polygroups are proved.

Paratopological polygroups versus topological polygroups

“…This concept was defined by Heidari et al [10] on topological semihypergroups. In [11], they studied topological polygroups P with this property .…”

“…We follow the terminology of [1,2,6,7,11,13]. The notion of hyperstructure, as a generalization of algebraic structure, was introduced by F. Mary at the 8th congress of Scandinavian Mathematicians in 1934 [19].…”

“…Recently, Heidari et al [11] defined the notion of topological polygroups and proved some properties. They also proved the isomorphism theorem of topological polygroups.…”

Graph product of generalized Cayley graphs over polygroups

“…Quasi-canonical hypergroups (called polygroups by Comer) were introduced in [2], as a generalization of canonical hypergroups, introduced in [16]. In [11] Heidari et al…”

On topological complete hypergroups

“…The year 1934 saw the raise of the concept of hyper roups by Marty [12], later it was studied by Corsini [2], Corsini and Leoreanu [3], Davvaz [4], Dresher and Ore [6], Freni [7], Koskas [11], Massouros [13], R. Migliorato [15], Mittas [14], Tallini [17], Vougiouklis [18], and many others. Till now, only a few papers treated the notion of topological hyperstructures, for example see [1,[8][9][10]16]. Heidari et al [8,9] introduced the concepts of topological hypergroups and topological polygroups, respectively.…”