Continuous extension in topological digital spaces

[EN] 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 planeMelin, E. (2008). Continuous extension in topological digital spaces. Applied General Topology. 9(1):51-66. doi:10.4995/agt.2008.1869.SWORD51669