Bewley's limiting approach to infinite dimensional economies with l.s.c. preferences

We examine the existence of quasi-equilibria in economies with a general topological commodity space and l.s.c. preferences by the limiting technique of Bewley [Bewley, T., 1972. Existence of equilibria in economies with infinitely many commodities. Journal of Economic Theory 4, 514-540]. However, there are two major difficulties in using Bewley's technique for such economies. To overcome these difficulties, we propose a class of new preferences, called bipolar preferences, and impose a strong l.s.c. assumption upon the economies. As a result, an existence theorem of quasi-equilibria in economies with a general topological commodity space and l.s.c. preferences is established.