Universality of the Epstein-Wang type structure

We prove that the type structure constructed in [Epstein, L., Wang, T., 1996. 'Belief about belief' without probabilities. Econometrica 64, 1343-1373] is a universal/terminal type structure into which every suitably regular type structure can be embedded. Moreover, it is unique up to a homeomorphism and every belief-complete type space can be mapped onto the universal one. We also show how our results help understand connections among several existing constructions.