Respected Sir,

 Thanks for your immediate reply.

A soft set FA on the universe U is defined by the set of ordered pairs FA = {(x, fA (x)): x ∈ E, fA (x) ∈ P (U)}, where fA : E → P (U ) such that fA (x) = ∅ if x does not belongs A. Here fA is called an approximate function of the soft set FA. The value of fA may be arbitrary, some of them may be empty, and some may have non empty intersection.

Instead of open and closed sets in the defnition of topological spaces we use the this soft open sets and closed sets then it is called a Soft topological spaces. also singleton set means a set contains only one point x ∈ X.

A point from the underlying set with a single parameter assume single value.