Bipolar Soft Topological Spaces

Abstract

Bipolar soft set theory is a mathematical tool associates between bipolarity and soft set theory, it is deï¬ned by two soft sets one of them gives us the positive information where the other gives us the negative. The goal of our paper is to deï¬ne the bipolar soft topological space on a bipolar soft set and study its basic notions and properties. We also investigate the deï¬nitions of: bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and establish some important properties on them. Some relations between them are also discussed. Moreover, the notions of bipolar soft point, bipolar soft limit point and the derived set of a bipolar soft set are discussed. In additions, examples are presented to illustrate our work.