Exchange economies are defined by a mapping between an atomless space of agents and a space of characteristics where the commodity space is a separable Banach space. We characterize equilibrium stability of economies relaying on the continuity of the equilibrium correspondence. We provide a positive answer to an open question about the continuity of the Walras correspondence in infinite dimensional spaces. In addition, we do not assume neither differentiability nor a fixed set of agents for the different economies, like it is usually assumed in the stability literature
