This note characterizes the set A¡∞ of actions of player ¡ that are uniquely rationalizable for some hierarchy of beliefs on an arbitrary space of uncertainty. It is proved that for any rationalizable action a¡ for the type t¡, if a¡ belongs to A¡∞ and is justified by conjectures concentrated on A-¡∞, then there exists a sequence of types converging to t¡ for which a¡ is uniquely rationalizable.