On Soft Topological Polygroups and Their Examples

Abstract

Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups.

A different look at the soft topological polygroups

“…In [8], R. Mousarezaei and B. Davvaz made a soft topological polygroup over a polygroup. The ideas presented in this article can be used to build more polygroups and more soft topological polygroup.…”

“…The efforts of many scientists were used in this direction, including G. Oguz [1], Heidari et al [2], Cagman et al [3], Wang et al [4], Shah and Shaheen [5], Davvaz [6], Maji [7], Mousarezaei and Davvaz [8], Nuzmul [9], and Hida [10]. Figure 1 shows the relations between polygroups, topology and soft sets, where each item is studied and investigated by many authors.…”

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

“…The family of all soft closed sets in (X, τ, A) will be denoted by τ c . Soft topological concepts and their applications are still a hot area of research ( [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). The notion of ω-regular TSs was introduced in [23], then the study of ω-regular TSs continued in [24] in which the authors defined and investigated ω-T 2 TSs.…”

Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

“…Then, many topological concepts were modified to include soft topology. The concepts of soft topology and their applications is still a hot area of research (see for example [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]).…”