Limit Continuity Differentiability

We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers we introduce concept of soft intervals. Boundedness of soft real sets is defined and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next we introduce the concepts of limit continuity and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano's theorem intermediate value property and fixed point theorem. Because the soft real numbers are not linearly ordered several twists in the arguments are required for proving those results. In the context of differentiability of functions some basic theorems like Rolle's theorem and Lagrange's mean value theorem are also extended in soft setting.