University of MaraghehSahand Communications in Mathematical Analysis2322-580704120161101On exponentiable soft topological spaces11422216ENGhasemMirhosseinkhaniDepartment of Mathematics, Sirjan University of Technology, Sirjan, Iran.AhmadMohammadhasaniDepartment of Mathematics, Sirjan University of Technology, Sirjan, Iran.Journal Article20150512An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalization of the category $mathbf{Top}$. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also we<br />give the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.http://scma.maragheh.ac.ir/article_22216_6c2f05eb0b9ad6ca148f19bd3ef7cb1d.pdf