ON SURFACES IN DIGITAL TOPOLOGY

In [Ayala∞] a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an easy way, definitions, statements and proofs from continuous topology to digital topology (see details in §2). In particular, it provides a straightforward definition of n-dimensional digital manifold. In this paper we prove that the class of digital 2-manifolds without boundary in the grid ZZ agrees with the class of (26, 6)-surfaces defined by Kong-Roscoe and other authors ([Morgenthaler81],[Reed84],[Kong85]). As a consequence, the separation theorem for digital surfaces stated in [Morgenthaler81] and [Reed84] is obtained.