DIGITAL COVERING THEORY AND ITS APPLICATIONS

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 4,  2008, pp.589-602
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.4.589
Title & Authors
DIGITAL COVERING THEORY AND ITS APPLICATIONS
Kim, In-Soo; Han, Sang-Eon;

Abstract
As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $\small{k_i}$-curves in $\small{{\mathbf{Z}}^n}$, $\small{i{\in}{1,2}}$.
Keywords
k-adjacency relations of $\small{{\mathbf{Z}}^n}$;digital continuity;geometric realization;relative k- homotopy;strong k-deformation retract;k-homotopic thinning;$\small{(k_0,k_1)}$-isomorphism;digital $\small{(k_0,k_1)}$-covering;discrete Deck's transformation group;universal $\small{(k_0,k_1)}$-covering;
Language
English
Cited by
1.
REGULAR COVERING SPACE IN DIGITAL COVERING THEORY AND ITS APPLICATIONS,;

호남수학학술지, 2009. vol.31. 3, pp.279-292
2.
COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3,;

호남수학학술지, 2010. vol.32. 1, pp.141-155
3.
KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS,;

대한수학회지, 2010. vol.47. 5, pp.1031-1054
4.
UTILITY OF DIGITAL COVERING THEORY,;;

호남수학학술지, 2014. vol.36. 3, pp.695-706
1.
UTILITY OF DIGITAL COVERING THEORY, Honam Mathematical Journal, 2014, 36, 3, 695
2.
COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3, Honam Mathematical Journal, 2010, 32, 1, 141
3.
REGULAR COVERING SPACE IN DIGITAL COVERING THEORY AND ITS APPLICATIONS, Honam Mathematical Journal, 2009, 31, 3, 279
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