A note on alternative digital topologies

AbstractThis paper contains a brief outline—in a form intended to clarify their interrelation—of four theories devised for the analysis of the topological attributes of a digital image. They are (i) Rosenfeld's combinatorial theory (to which he gave the name “digital topology”), (ii) the generalization of this due to Kong and Roscoe, (iii) Khalimsky, Kopperman and Meyer's theory of sets embedded in a locally finite space and (iv) the theory which results from choosing a specific model for the process by which the digital image is produced

The Jordan curve theorem in the Khalimsky plane

[EN] The connectivity in Alexandroff topological spaces is equivalent to the path connectivity. This fact gets some specific properties to Z2, equipped with the Khalimsky topology. This allows a sufficiently precise description of the curves in Z2 and permit to prove a digital Jordan curve theorem in Z2.Bouassida, E. (2008). The Jordan curve theorem in the Khalimsky plane. Applied General Topology. 9(2):253-262. doi:10.4995/agt.2008.1805.SWORD2532629