The Jordan curve theorem in the Khalimsky plane


  • Ezzeddine Bouassida University of Sfax



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


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.


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Author Biography

Ezzeddine Bouassida, University of Sfax

Faculty of Scienses of Sfax, Departement of Mathematics.


F. G. Arenas, Alexandroff spaces, Acta Math. Univ. Comenianea, vol. LXVIII, 1 (1999), 17–25.

E. Bouacida, O. Echi and E. Salhi, Topologies associées à une relation binaire et relation binaire spectrale, Boll. Mat. Ital., VII. Ser., B 10 (1996), 417–439.

E. Bouacida and N. Jarboui, Connectivity in A-spaces, JP Journal of Geometry and Topology. 7 (2007), 309–320.

N. Bourbaki, Topologie générale. Elément de mathématique, premiére partie, livre III, chapitr 1-2, Tird edition. Paris: Hermann.

E. D. Khalimsky, R. Kopperman and P. R. Meyer, Computer graphics and connected topologies on finite closed sets, Topology Appl. 36 (1967), 1–17.

C. O. Kisselman, Digital Jordan Curve Theorems, Lecture Notes in Computer Science, Springer, Berlin, vol. 1953 (2000).

C. O. Kisselman, Digital Geometry and Mathematical Morphology, Lecture Notes, Uppsala University, Departement of Mathematics, (2002).

T. Y. Kong, R. Kopperman and P. R. Meyer, A topological approach to digital topology, American. Math. Monthly. 98 (1991), 901–917.

J. Slapal, Digital Jordan Curves, Topology Appl. 153 (2006), 3255–3264.


How to Cite

E. Bouassida, “The Jordan curve theorem in the Khalimsky plane”, Appl. Gen. Topol., vol. 9, no. 2, pp. 253–262, Oct. 2008.