The basic of bipolar soft set theory stands for a mathematical instrument that bringstogether the soft set theory and bipolarity. Its definition is based on two soft sets, a set thatprovides positive information and other that gives negative. This paper mainly aims at defininga new bipolar soft generalized topological space; setting out of the point that the collection ofbipolar soft sets forms the basis for the definition of the new concept is defined. Added to that,an investigation has been made of the four concepts of bipolar soft generalized, namely g-interior,g-closure, g-exterior and g-boundary. Furthermore, the main properties of bipolar soft generalizedtopological space (BSGT S) are established. This paper also attends to the discussion of therelations between these new definitions and the application of the given bipolar soft generalizedtopological spaces in a decision-making problem where an algorithm for this application has beensuggested. Finally, to clarify and substantiate what the current work subsumes, some exampleshave been provided.

In this paper, we apply the concept of soft sets to δ-open set and δ-closed set. The associated soft δ-topology in terms of soft δ-open sets were introduced and some properties of them were investigated. Moreover, the definitions, characterizations and basic results concerning soft δ-interior, soft δ-closure, soft δ-boundary and soft δ-exterior were given. Finally, the concept of soft pu−δ- continuity was defined and some properties of it were introduced.

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: BS g-interior point, BS g-exterior point, BS g-boundary point, BS g-neighborhood point and basis on BSGT S. Finally, we give comparisons among these concepts of bipolar soft generalized topological spaces (BSGT S) by using bipolar soft point (BSP). Each concept introduced in this paper is explained with clear examples.

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The objective of studing the current paper is to introduced a new class of soft open sets in soft topological spaces called soft -open sets. Then soft -open sets are used to study some soft topological concepts. Furthermore, the concept of soft -continuous and almost soft -continuous functions are defined by using the soft -open sets. Some properties and Characterizations of such functions are given.