Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

Abstract

The concept of soft set theory can be used as a mathematical tool for dealing with problems that contain uncertainty. Then, a new mixed mathematical model called the bipolar soft set is created by merging soft sets and bipolarity, which gave the concept of a binary model of grading. Bipolar soft set is characterized by two soft sets, one of which provides positive information and the other negative. Bipolar soft generalized topology is a generalization of bipolar soft topology. The importance of limit points in all branches of mathematics cannot be ignored. It forms one of the most significant and fundamental concepts in topology. On this basis, the derived set concept is required in the establishment and continuation of some properties. Accordingly, the limit point in bipolar soft generalized theory is defined. In this paper, we present the notion of bipolar soft generalized limit points. We explained the relation between the bipolar soft generalized derived and the bipolar soft generalized closure set. Added to that, we discussed some structures of a bipolar soft generalized topological space such as: <img src=image/13428354_01.gif>-interior point, <img src=image/13428354_01.gif>-exterior point, <img src=image/13428354_01.gif>-boundary point, <img src=image/13428354_01.gif>-neighborhood point and basis on <img src=image/13428354_02.gif>. Finally, we give comparisons among these concepts of bipolar soft generalized topological spaces (<img src=image/13428354_02.gif>) by using bipolar soft point (<img src=image/13428354_03.gif>). Each concept introduced in this paper is explained with clear examples.