COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 1,  2015, pp.135-147
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.1.135
Title & Authors
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT
Han, Sang-Eon;

Abstract
Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $\small{L_S}$- and the $\small{L_C}$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $\small{k_i}$-curves with $\small{l_i}$ elements in $\small{Z^{n_i}}$, $\small{i{\in}\{1,2\}}$ denoted by $\small{SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}}$. Since a normal adjacency for this product and the $\small{L_C}$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $\small{Z^{n_1+n_2}}$ and another adjacency satisfying the $\small{L_C}$-property? This research plays an important role in studying product properties of digital topological properties.
Keywords
digital topology;digital covering space;digital isomorphism;digital product;Cartesian adjacency;normal adjacency;S-compatible;digital topology;digital product;$\small{L_S}$-;$\small{L_C}$-property;
Language
English
Cited by
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