We show that any complete, lower-semicontinuous, and translation- invariant preorder defined on a topological vector space admits a linear and continuous utility representation.

The purpose of this addendum is to correct some results published in our paper "Some issues related to the topological aggregation of preferences" (SCW (1992) 9: 213-227). <!--ID="" Acknowledgements. Thanks are given to Prof. Boris A. Efimov and Gleb A. Koshevoy (Moskow, Russia), Luc Lauwers (Leuven, Belgium) and Michael Sunderland (Oxford, U.K.) for their valuable suggestions and comments.-->

Necessary and sufficient conditions are presented for the existence of a pair u,v of positively homogeneous of degree one real functions representing an interval order [InlineMediaObject not available: see fulltext.] on a real cone K in a topological vector space E (in the sense that, for every...

It is shown that any completely preordered topological real algebra admits a continuous utility representation which is an algebra-homomorphism (i.e., it is linear and multiplicative). As an application of this result, we provide an algebraic characterization of the projective (dictatorial)...