Continuous extension in topological digital spaces

Erik Melin


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.


Khalimsky topology; Digital geometry; Alexandrov space; Continuous extension

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1. Digital Khalimsky Manifolds
Erik Melin
Journal of Mathematical Imaging and Vision  vol: 33  issue: 3  first page: 267  year: 2009  
doi: 10.1007/s10851-008-0114-1

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