A framework for digital topology

Abstract

The main goal of this paper is to show the functional architecture of a framework for digital topology. This architecture has four levels, called device, logical, conceptual and continuous levels. In each one of them one can use several models according to the particular problem. The models in the device level represent the physical problem whereas the models in the continuous level are topological spaces which allow one to use the well-known results of continuous topology (actually, the stronger results of polyhedral topology). The other two levels are used to find a digital solution. The logical level is closer to the device level and it is used for processing, for writing algorithms and showing their correctness. The conceptual level is the nearest to the continuous level and it is used to translate results and notions from the continuous level to the logical leve