Continuous extension in topological digital spaces | Zendy

Erik Melin | Zendy

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Continuous extension in topological digital spaces

Author(s) -

Erik Melin

Publication year - 2008

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2008.1869

Subject(s) - mathematics , extension (predicate logic) , topological space , continuous function (set theory) , space (punctuation) , plane (geometry) , real line , function space , pure mathematics , function (biology) , topology (electrical circuits) , discrete mathematics , combinatorics , geometry , computer science , evolutionary biology , biology , programming language , operating system

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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