On exponentiable soft topological spaces

An object XX of a category CC with finite limits is called exponentiable if the functor −×X:C→C−×X:C→C has a right adjoint. There are many characterizations of the exponentiable spaces in the category TopTop of topological spaces. Here, we study the exponentiable objects in the category STopSTop of soft topological spaces which is a generalization of the category TopTop. 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.