The theory of manifolds from the non-deterministic point of view

Summary Using the methods of non-deterministic analysis it is possible to define in a differentiable manifold a special structure called Gauss structure which allows one to study differentiable maps from one manifold into another without the use of local charts. The main theorem in this paper shows how it is possible to locally recover the jacobian of such maps by using the Gauss structures defined in the manifolds in question.