In the years 1977 and 1986, Khalimsky, and more recently Kovalevsky (1988), have shown that the digital images are associated to topological notions. Since then, the notions of general topology had been used in the processing of digital images. In this context, one of the more useful topologies is the Khalimsky’s topology. The aim of this work is to categorize the Khalimsky’s topological space taking as a starting point the properties of the spaces of Alexandroff.