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REMARKS ON DIGITAL PRODUCTS WITH NORMAL ADJACENCY RELATIONS
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 3,  2013, pp.515-524
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.3.515
 Title & Authors
REMARKS ON DIGITAL PRODUCTS WITH NORMAL ADJACENCY RELATIONS
Han, Sang-Eon; Lee, Sik;
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 Abstract
To study product properties of digital spaces, we strongly need to formulate meaningful adjacency relations on digital products. Thus the paper [7] 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 [4] and restates Theorem 6.4 of the paper [19].
 Keywords
digital topology;digital product;digital continuity;normal adjacency;digital covering space;
 Language
English
 Cited by
1.
AN EQUIVALENT PROPERTY OF A NORMAL ADJACENCY OF A DIGITAL PRODUCT,;

호남수학학술지, 2014. vol.36. 1, pp.199-215 crossref(new window)
2.
UTILITY OF DIGITAL COVERING THEORY,;;

호남수학학술지, 2014. vol.36. 3, pp.695-706 crossref(new window)
3.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT,;

호남수학학술지, 2015. vol.37. 1, pp.135-147 crossref(new window)
4.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY,;;

호남수학학술지, 2015. vol.37. 4, pp.577-593 crossref(new window)
1.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY, Honam Mathematical Journal, 2015, 37, 4, 577  crossref(new windwow)
2.
Generalizations of continuity of maps and homeomorphisms for studying 2D digital topological spaces and their applications, Topology and its Applications, 2015, 196, 468  crossref(new windwow)
3.
UTILITY OF DIGITAL COVERING THEORY, Honam Mathematical Journal, 2014, 36, 3, 695  crossref(new windwow)
4.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT, Honam Mathematical Journal, 2015, 37, 1, 135  crossref(new windwow)
5.
AN EQUIVALENT PROPERTY OF A NORMAL ADJACENCY OF A DIGITAL PRODUCT, Honam Mathematical Journal, 2014, 36, 1, 199  crossref(new windwow)
 References
1.
C. Berge, Graphs and Hypergraphs, 2nd ed., North-Holland, Amsterdam, 1976.

2.
L. Boxer, Digitally continuous functions, Pattern Recognition Letters, 15 (1994), 833-839. crossref(new window)

3.
L. Boxer, Digital Products, Wedge; and Covering Spaces, Jour. of Mathematical Imaging and Vision, 25 (2006), 159-171. crossref(new window)

4.
L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences, 11(4) (2012), 161-179.

5.
A. Bretto, Comparability graphs and digital topology, Computer Vision and Imaging Understanding, 82 (2001), 33-41. crossref(new window)

6.
S.E. Han, Computer topology and its applications, Honam Math. Jour. 25(1) (2003), 153-162.

7.
S.E. Han, Non-product property of the digital fundamental group, Information Sciences, 171(1-3) (2005), 73-91. crossref(new window)

8.
S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal, 27(1) (2005), 115-129.

9.
S.E. Han, Erratum to /Non-product property of the digital fundamental group", Information Sciences, 176(1) (2006), 215-216. crossref(new window)

10.
S.E. Han, Equivalent ($k_0,k_1$)-covering and generalized digital lifting, Information Sciences, 178(2) (2008), 550-561. crossref(new window)

11.
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. crossref(new window)

12.
S.E. Han, Cartesian product of the universal covering property, Acta Applicandae Mathematicae, 108 (2009), 363-383. crossref(new window)

13.
S.E. Han, Regural covering space in digital covering theory and its applications, Honam Mathematical Journal, 31(3) (2009), 279-292. crossref(new window)

14.
S.E. Han, Remark on a generalized universal covering space, Honam Mathematical Jour. 31(3) (2009), 267-278. crossref(new window)

15.
S.E. Han, KD-($k_0,k_1$)-homotopy equivalence and its applications, Journal of Korean Mathematical Society, 47(5) (2010), 1031-1054. crossref(new window)

16.
S.E. Han, Multiplicative property of the digital fundamental group, Acta Applicandae Mathematicae, 110(2) (2010), 921-944. crossref(new window)

17.
S.E. Han, Ultra regular covering space and its automorphism group, International Journal of Applied Mathematics & Computer Science, 20(4) (2010), 699-710.

18.
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).

19.
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. crossref(new window)

20.
T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.

21.
A. Rosenfeld, Continuous functions on digital pictures, Pattern Recognition Letters, 4 (1986), 177-184. crossref(new window)