Continuous Extension in Topological Digital Spaces
نویسنده
چکیده
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 → Z can be extended to all of X. We also consider the more general case of mappings X → Y between smallest-neighborhood spaces, and prove a digital version of the no-retraction theorem.
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