Construction of a continuous utility function for a class of preferences

We construct a continuous utility indicator for a subclass of continuous preference relations, including some with thick indifference classes, using a measure theoretic technique related to that of Neuefeind (1972). This indicator is not continuous on the full class of continuous preferences endowed with the closed convergence topology. It appears that no such indicator can be constructed, although Mas-Colell (1975) has established that one exists. A finer topology for preferences seems appropriate.