Topological complexities of finite digital images
محورهای موضوعی : Algebraic topology
1 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey
2 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey
کلید واژه: Topological complexity, higher topological complexity, digital topology,
چکیده مقاله :
Digital topological methods are often used in computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a digitally connected finite digital image. We present all possible cases of the topological complexity TC of a finite digital image in $\mathbb{Z}$ and $\mathbb{Z}^{2}$. Finally, we determine the higher topological complexity TC$_{n}$ of finite irreducible digital images independently of the number of points for $n > 1$.
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