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