Unfolding of smooth differential topological space

ABSTRACT:In this article we will introduce the conditions under which the folding of the cartesian product of two smooth topological spaces will be a smooth topological space or not a smooth one. Also, the conditions under which the unfolding of two smooth topological spaces will be a smooth topological space or not. The relation between the unfoldings and the diffeomorphisms will be a achieved. Some commutative diagrams are deduced. The limits of foldings and unfoldings are presented. The end of the foldings and the unfolding are obtained