Additive Utility

We put the theory of cardinal and additive utilities on the same kind of simple foundation as the theory of ordinal utility. We give necessary and sufficient conditions for preferences to have continuous cardinal or additive utility functions, on connected topological spaces. Basing our proofs on fundamental algebraic theorems yields new techniques that allow us to give simple proofs of earlier results (cf. [4, 14] and to provide a basis for new results [10].