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.

This research aims to study some algebraic curve behaviors in monad (halo) of the regular and irregular points. For this, the Robinson ideas can be used for limited points. Also the geometric tangent at this limited point and the analysis of the algebraic curve around the same point will be studied. Concepts of nonstandard analysis given by Robinson and its axiomatic by Nelson have been used. In this research, we have obtained a state where the point of origin is a regular point and concave is as illustrated in (5). So the curve has connection in this equation (6). There is a second state where the point of origin is an abnormal point of the curve as illustrated in (11). Finally, it has a concave that is calculated in the equation (29).