  In this paper we study speedups of dynamical systems in the topological
category. Specifically, we characterize when one minimal homeomorphism on a
Cantor space is the speedup of another. We go on to provide a characterization
for strong speedups, i.e., when the jump function has at most one point of
discontinuity. These results provide topological versions of the
measure-theoretic results of Arnoux, Ornstein and Weiss, and are closely
related to Giordano, Putnam and Skau's characterization of orbit equivalence
for minimal Cantor systems.
