Extension of continuous functions in digital spaces with the Khalimsky topology

The digital space Z n equipped with Efim Khalimskyʹs topology is a connected space. We study continuous functions Z n ⊃ A → Z , from a subset of Khalimsky n-space to the Khalimsky line. We give necessary and sufficient condition for such a function to be extendable to a continuous function Z n → Z . We classify the subsets A of the digital plane such that every continuous function A → Z can be extended to a continuous function on the whole plane.