REMARKS ON DIGITAL PRODUCTS WITH NORMAL ADJACENCY RELATIONS Han, Sang-Eon; Lee, Sik;
To study product properties of digital spaces, we strongly need to formulate meaningful adjacency relations on digital products. Thus the paper  firstly developed a normal adjacency relation on a digital product which can play an important role in studying the multiplicative property of a digital fundamental group, and product properties of digital coverings and digitally continuous maps. The present paper mainly surveys the normal adjacency relation on a digital product, improves the assertion of Boxer and Karaca in the paper  and restates Theorem 6.4 of the paper .
digital topology;digital product;digital continuity;normal adjacency;digital covering space;
L. Boxer, Digital Products, Wedge; and Covering Spaces, Jour. of Mathematical Imaging and Vision, 25 (2006), 159-171.
L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences, 11(4) (2012), 161-179.
A. Bretto, Comparability graphs and digital topology, Computer Vision and Imaging Understanding, 82 (2001), 33-41.
S.E. Han, Computer topology and its applications, Honam Math. Jour. 25(1) (2003), 153-162.
S.E. Han, Non-product property of the digital fundamental group, Information Sciences, 171(1-3) (2005), 73-91.
S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal, 27(1) (2005), 115-129.
S.E. Han, Erratum to /Non-product property of the digital fundamental group", Information Sciences, 176(1) (2006), 215-216.
S.E. Han, Equivalent ($k_0,k_1$)-covering and generalized digital lifting, Information Sciences, 178(2) (2008), 550-561.
S.E. Han, The k-homotopic thinning and a torus-like digital image in $Z^n$, Journal of Mathematical Imaging and Vision, 31(1) (2008), 1-16.
S.E. Han, Cartesian product of the universal covering property, Acta Applicandae Mathematicae, 108 (2009), 363-383.
S.E. Han, Regural covering space in digital covering theory and its applications, Honam Mathematical Journal, 31(3) (2009), 279-292.
S.E. Han, Remark on a generalized universal covering space, Honam Mathematical Jour. 31(3) (2009), 267-278.
S.E. Han, KD-($k_0,k_1$)-homotopy equivalence and its applications, Journal of Korean Mathematical Society, 47(5) (2010), 1031-1054.
S.E. Han, Multiplicative property of the digital fundamental group, Acta Applicandae Mathematicae, 110(2) (2010), 921-944.
S.E. Han, Ultra regular covering space and its automorphism group, International Journal of Applied Mathematics & Computer Science, 20(4) (2010), 699-710.
S.E. Han and B.G. Park, Digital graph ($k_0,k_1$)-isomorphism and its applications, http://atlas-conferences.com/c/a/k/b/36.htm(2003).
S.E. Han, A. Sostak, A compression of digital images derived from a Khalimksy topological structure, Computational and Applied Mathematics, http://dx.doi.org/[DOI], DOI: 10.1007/s40314-013-0034-6, Online first, in press.
T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.
A. Rosenfeld, Continuous functions on digital pictures, Pattern Recognition Letters, 4 (1986), 177-184.