Continuous extension in topological digital spaces
DOI:
https://doi.org/10.4995/agt.2008.1869Keywords:
Khalimsky topology, Digital geometry, Alexandrov space, Continuous extensionAbstract
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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