Continuous extension in topological digital spaces

Erik Melin

Abstract

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.


Keywords

Khalimsky topology; Digital geometry; Alexandrov space; Continuous extension

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References

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