Good Pairs of Adjacency Relations in Arbitrary Dimensions

Abstract: In this text we show, that the notion of a "good pair" that was introduced in the paper "Digital Manifolds and the Theorem of Jordan-Brouwer" has actually known models. We will show, how to choose cubical adjacencies, the generalizations of the well known 4- and 8-neighborhood to arbitrary dimensions, in order to find good pairs. Furthermore, we give another proof for the well known fact that the Khalimsky-topology implies good pairs. The outcome is consistent with the known theory as presented by T.Y. Kong, A. Rosenfeld, G.T. Herman and M. Khachan et.al and gives new insights in higher dimensions.