Extension of continuous functions in digital spaces with the Khalimsky topology |
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Authors: | Erik Melin |
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Affiliation: | Uppsala University, Department of Mathematics, Box 480, SE-751 06 Uppsala, Sweden |
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Abstract: | The digital space Zn equipped with Efim Khalimsky's topology is a connected space. We study continuous functions Zn⊃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 Zn→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. |
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Keywords: | primary, 54C20 secondary, 54C05, 54D05, 54D10 |
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