KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS

Title & Authors
KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS
Han, Sang-Eon;

Abstract
Let $\small{\mathbb{Z}^n}$ be the Cartesian product of the set of integers $\small{\mathbb{Z}}$ and let ($\small{\mathbb{Z}}$, T) and ($\small{\mathbb{Z}^n}$, $\small{T^n}$) be the Khalimsky line topology on $\small{\mathbb{Z}}$ and the Khalimsky product topology on $\small{\mathbb{Z}^n}$, respectively. Then for a set $\small{X\;{\subset}\;\mathbb{Z}^n}$, consider the subspace (X, $\small{T^n_X}$) induced from ($\small{\mathbb{Z}^n}$, $\small{T^n}$). Considering a k-adjacency on (X, $\small{T^n_X}$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $\small{T^n_X}$) :
Keywords
computer topology;digital topology;digital space;KD-($\small{k_0}$, $\small{k_1}$)-continuity;KD-k-deformation retract;digital homotopy equivalence;KD-($\small{k_0}$, $\small{k_1}$)-homotopy equivalence;KD-k-homotopic thinning;
Language
English
Cited by
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