In this paper we present some geometrical and topological concepts to accommodate the needs of information theories. It is demonstrated that image processing methods and algorithms are well correlated with various aspects of the notion of P-scattered space, where P is a given property. Theorem 2.8 illustrates how the P-scatteredness concept can be explored through mathematical induction, which opens the possibilities to apply algorithmic procedures. It is established that the Khalimsky topology on the discrete line is unique as the minimal symmetric digital topology on Z.