Numerical representation of countably bounded preferences

The countable-boundedness property characterizes the complete preorders, de fined on path-connected topological spaces, which are representable by a ut ility function. We extend this concept to pseudotransitive preferences or, more generally, interdependent preferences and we show that the countable b oundedness is a necessary condition for the existence of representation by two numerical functions. Moreover, for a class of spaces more general than the path-connected topological spaces, we use that property to obtain neces sary and sufficient conditions for the representation of a preference by tw o numerical functions. This characterization generalizes several results on representation of preferences.