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.