  A point of a digital space is called simple if it can be deleted from the
space without altering topology. This paper introduces the notion simple set of
points of a digital space. The definition is based on contractible spaces and
contractible transformations. A set of points in a digital space is called
simple if it can be contracted to a point without changing topology of the
space. It is shown that contracting a simple set of points does not change the
homotopy type of a digital space, and the number of points in a digital space
without simple points can be reduces by contracting simple sets. Using the
process of contracting, we can substantially compress a digital space while
preserving the topology. The paper proposes a method for thinning a digital
space which shows that this approach can contribute to computer science such as
medical imaging, computer graphics and pattern analysis.
