  This paper presents six theorems and ten propositions that can be read as
deconstructing and integrating the continuity postulate under the rubric of
pioneering work of Eilenberg, Wold, von Neumann-Morgenstern, Herstein-Milnor
and Debreu. Its point of departure is the fact that the adjective continuous
applied to a function or a binary relation does not acknowledge the many
meanings that can be given to the concept it names, and that under a variety of
technical mathematical structures, its many meanings can be whittled down to
novel and unexpected equivalences that have been missed in the theory of
choice. Specifically, it provides a systematic investigation of the two-way
relation between restricted and full continuity of a function and a binary
relation that, under convex, monotonic and differentiable structures, draws out
the behavioral implications of the postulate.
