ON THE PRIMITIVES OF IFFERENTIAL ONE-MAPS

If a i .erential one-map between normed spaces is continuous on a star-like open set an is i .erentiable possibly except of one point then it has a primitive if an only if its erivative as a bilinear form is symmetric at every point where it exists.A generalization of the theorem on the existence of the potential operator is also obtained.The proof is based on the idea of the Goursat Lemma.