Using arithmetic jet spaces we attach perfectoid to smooth schemes and morphisms of perfectoidspaces $\\delta$-morphisms schemes. We also study attached differential equations defined by some the remarkable appearing in theory such as $\\delta$-charactersof elliptic curves $\\delta$-period maps on modular curves.

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...