Soft Bornological Group Acts on Soft Bornological Set

Ashwaq F. Abdal; Anwar N. Imran; Alaa A. Najm aldin; Amal O. Elewi

doi:10.24996/ijs.2023.64.2.28

Authors

Ashwaq F. Abdal Department of Mathematic, College of Science, University of Diyala, Diyala, Iraq https://orcid.org/0000-0001-8495-8870
Anwar N. Imran Department of Mathematic, College of Science, University of Diyala, Diyala, Iraq
Alaa A. Najm aldin Department of Mathematic, College of Science, University of Diyala, Diyala, Iraq
Amal O. Elewi Department of Mathematic, College of Science, University of Diyala, Diyala, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.2.28

Keywords:

Soft set, Bounded map, Soft bornological group, Soft bornological set, Soft bounded set

Abstract

In this paper, we introduce the notation of the soft bornological group to solve the problem of boundedness for the soft group. We combine soft set theory with bornology space to produce a new structure which is called soft bornological group. So that both the product and inverse maps are soft bounded. As well as, we study the actions of the soft bornological group on the soft bornological sets. The aim soft bornological set is to partition into orbital classes by acting soft bornological group on the soft bornological set. In addition, we explain the centralizer, normalizer, and stabilizer in details. The main important results are to prove that the product of soft bornological groups is soft bornological group and the action for different elements are the same actions.