  We study topological mixing properties and the maximal equicontinuous factor
of rank-one subshifts as topological dynamical systems. We show that the
maximal equicontinuous factor of a rank-one subshift is finite. We also
determine all the finite factors of a rank-one shift with a condition involving
the cutting and spacer parameters. For rank-one subshifts with bounded spacer
parameter we completely characterize weak mixing and mixing. For rank-one
subshifts with unbounded spacer parameter we prove some sufficient conditions
for weak mixing and mixing. We also construct some examples showing that the
characterizations for the bounded spacer parameter case do not generalize to
the unbounded spacer parameter case.
