Expected Utility Without Assuming Continuity

I provide an axiomatization of expected utility in which topological continuity is replaced by a geometric axiom.

The axiom requires a finite set of indifferent lotteries that span a hyperplane.

In the case of three prizes, two indifferent lotteries suffice.

The axiom is weaker than Solvability, as well as logically independent of Weak Continuity and the Archimedean axiom.