About manifolds and determinacy in general equilibrium theory

In this paper we prove that the social equilibrium set, of an exchange economy, with consumption space as a subset of a Banach space in a Banach manifold, and this Characterization does not depend on the number of commodities. In the way to obtain this characterization we will show that the set of social weights of equilibrium, associated with a giben distribution of the initial endowments, is finite.Banach Space, Banach Manifold, General Equilibrium, Equilibrium Social Weights.