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In this paper, we construct a universal type space for a class of possibility models by imposing topological restrictions on the players' beliefs. Along the lines of Mertens and Zamir [International Journal of Game Theory, 14 (1985) 1] or Brandenburger and Dekel [Journal of Economic Theory 59 (1993) 189], we show that the space of all hierarchies of compact beliefs that satisfy common knowledge of coherency (types) is canonically homeomorphic to the space of compact beliefs over the state ofdoi:10.1016/j.jmateco.2003.11.009 fatcat:vguxdqym6ff4vfgpgkyfebsu4u