Continuity postulates and solvability axioms in economic theory and in mathematical psychology: a consolidation of the theory of individual choice

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of (full, separate, Wold, weak Archimedean, mixture) with those (restricted, unrestricted) the completeness transitivity a binary relation. 2 uses primitive notion separately continuous function answer question when an analogous property on relation is fully continuous. 3 provides portmanteau theorem equivalence between restricted various monotonicity. Finally, 4 variant follows dispensing dimensionality requirement providing partial equivalences notions. These are motivated for their potential use representation theorems.