  In intuitionistic mathematics, the Brouwer Continuity Theorem states that all
total real functions are (uniformly) continuous on the unit interval. We study
this theorem and related principles from the point of view of Reverse
Mathematics over a base theory accommodating higher types and Nonstandard
Analysis. With regard to the bigger picture, Reverse Mathematics provides a
classification of theorems of ordinary mathematics based on computability. Our
aim is to provide an alternative classification of theorems based on the
central tenet of Feferman's Explicit Mathematics}, namely that a proof of
existence of an object yields a procedure to compute said object. Our
classification gives rise to the Explicit Mathematics theme (EMT). Intuitively
speaking, the EMT states that a standard object with certain properties can be
computed by a functional if and only if this object exists classically with
these same standard and nonstandard properties. Hence, we establish the EMT for
a series of intuitionistic principles in this paper.
