Digitizations preserving shape

摘要

We show in this paper how it is possible to digitize a wide class of planar compacta (i.e. bounded and closed subsets of the plane) in such a way that their digitizations have the same shape, in the sense of Borsuk, as the original set. This class is formed by all those compacta having the shape of finite polyhedra. As a corollary we obtain that for a still wide subclass, the homotopy properties are also preserved under appropriate digitizations. Moreover, we show that if a set does not have the shape of a finite polyhedron, there is no possible digitization that is shape preserving.