Open AccessThe higher topological complexity in digital images
Author(s) -
Melih İs,
İsmet Karaca
Publication year - 2020
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.2020.13553
Subject(s) - mathematics , topological complexity , homotopy , topology (electrical circuits) , algebraic topology , digital topology , algebraic number , digital image , pure mathematics , topological space , image (mathematics) , combinatorics , artificial intelligence , computer science , general topology , extension topology , image processing , mathematical analysis
Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy. These properties can also be useful for the future works in some applications of algebraic topology besides topological robotics. Moreover, we show that the cohomological lower bounds for the digital topological complexity TC(X,κ) do not hold.
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