Coincidence Point Sets in Digital Topology

Abstract

In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not be analogous to the classical topological fixed point theory. We also introduce and study some topological invariants related to the coincidence and common fixed point sets for continuous maps on a digital image. Moreover, we study how these coincidence point sets are affected by rigidity and deformation retraction. Lastly, we present briefly a concept of divergence degree of a point in a digital image.