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This paper presents four theorems that connect continuity postulates inmathematical economics to solvability axioms in mathematical psychology, andranks them under alternative supplementary assumptions. Theorem 1 connectsnotions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture)with those of solvability (restricted, unrestricted) under the completeness andtransitivity of a binary relation. Theorem 2 uses the primitive notion of aseparately-continuous function to answer the question when an analogousproperty on a relation is fully continuous. Theorem 3 provides a portmanteautheorem on the equivalence between restricted solvability and various notionsof continuity under weak monotonicity. Finally, Theorem 4 presents a variant ofTheorem 3 that follows Theorem 1 in dispensing with the dimensionalityrequirement and in providing partial equivalences between solvability andcontinuity notions. These theorems are motivated for their potential use inrepresentation theorems.

Continuity Postulates and Solvability Axioms in Economic Theory and in Mathematical Psychology: A Consolidation of the Theory of Individual Choice