The equilibrium set of infinite dimensional Walrasian economies and the natural projection

The natural projection plays a fundamental role to understand the behavior of the Walrasian economies. In this paper, we extend this method to analyze the behavior of infinite dimensional economies. We introduce the definition of the social equilibrium set, and we show that there exists a bijection between this set and the Walrasian equilibrium set of an infinite dimensional economy. In order to describe the main topological characteristics of both sets, we analyze the main differential characteristics of the excess utility function and then, we extend the method of the natural projection as suggested by Y. Balasko.