On exponentiable soft topological spaces

An object X of a category C with finite limits is called exponentiable if the functor −×X:C→C has a right adjoint. There are many characterizations of the exponentiable spaces in the category Top of topological spaces. Here, we study the exponentiable objects in the category STop of soft topological spaces which is a generalization of the category Top. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also we give the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.