The Jordan curve theorem in the Khalimsky plane

Ezzeddine Bouassida


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.


Topological space; Alexandroff topology; Khalimsky topology; Simple closed curve; Jordan curve theorem

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