The genericity of the McAfee-Reny condition for full surplus extraction in models with a continuum of types

McAfee and Reny (1992) have given a necessary and sufficient condition for full surplus extraction in models with a continuum of types. We interpret their condition as significantly stronger version of the requirement of injectiveness of the function mapping abstract types into beliefs and prove that their condition is satisfied by a generic set of model specifications. Our analysis involves an extension of the classical embedding theorem for continuous functions. Our proof does not rely on finite approximations and the topology on beliefs that we use is compatible with strategic continuity.