Let SoftSet be the category of soft sets and soft mappings, where a soft mapping (f; e) : (F;A) ! (G;B) from a soft set (F;A) over X to soft set (G;B) over Y is a pair of functions f : X-> Y and e : A -> B such that Ps(f) ◦ G ◦ e ⪯ F, where Ps is the contravariant powerset functor. Let S(A;X) = {(F;A)|F : A -> P(X)g be the set of soft sets whit parameter A over set X. The soft set (H;A) is said to be a soft subset of (F;A) whenever H(a) is a subset of F(a) for each a in A. consider SS(F;A) is the family of all soft subsets of (F;A). The inclusion map t_X : TX c_> P(X) is a topology over X whenever T_X containing X and emptyset and closed under finite intersections and arbitrary unions.
