Continuous extension in topological digital spaces


  • Erik Melin Uppsala University



Khalimsky topology, Digital geometry, Alexandrov space, Continuous extension


We give necessary and sufficient conditions for the existence of a continuous extension from a smallest-neighborhood space (Alexandrov space) X to the Khalimsky line. Using this result, we classify the subsets A  X such that every continuous function A ! Zbcan be extended to all of X. We also consider the more general case ofbmappings X ! Y between smallest-neighborhood spaces, and prove abdigital no-retraction theorem for the Khalimsky plane.


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Author Biography

Erik Melin, Uppsala University

Department of Mathematics


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How to Cite

E. Melin, “Continuous extension in topological digital spaces”, Appl. Gen. Topol., vol. 9, no. 1, pp. 51–66, Apr. 2008.



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