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UTILITY OF DIGITAL COVERING THEORY
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  • Journal title : Honam Mathematical Journal
  • Volume 36, Issue 3,  2014, pp.695-706
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2014.36.3.695
 Title & Authors
UTILITY OF DIGITAL COVERING THEORY
Han, Sang-Eon; Lee, Sik;
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 Abstract
Various properties of digital covering spaces have been substantially used in studying digital homotopic properties of digital images. In particular, these are so related to the study of a digital fundamental group, a classification of digital images, an automorphism group of a digital covering space and so forth. The goal of the present paper, as a survey article, to speak out utility of digital covering theory. Besides, the present paper recalls that the papers [1, 4, 30] took their own approaches into the study of a digital fundamental group. For instance, they consider the digital fundamental group of the special digital image (X, 4), where X := which is a simple closed 4-curve with eight elements in , as a group which is isomorphic to an infinite cyclic group such as (Z, +). In spite of this approach, they could not propose any digital topological tools to get the result. Namely, the papers [4, 30] consider a simple closed 4 or 8-curve to be a kind of simple closed curve from the viewpoint of a Hausdorff topological structure, i.e. a continuous analogue induced by an algebraic topological approach. However, in digital topology we need to develop a digital topological tool to calculate a digital fundamental group of a given digital space. Finally, the paper [9] firstly developed the notion of a digital covering space and further, the advanced and simplified version was proposed in [21]. Thus the present paper refers the history and the process of calculating a digital fundamental group by using various tools and some utilities of digital covering spaces. Furthermore, we deal with some parts of the preprint [11] which were not published in a journal (see Theorems 4.3 and 4.4). Finally, the paper suggests an efficient process of the calculation of digital fundamental groups of digital images.
 Keywords
digital topology;digital product;k-homotopic thinning;normal adjacency;S-compatible adjacency;digital covering space;C-property;S-property;
 Language
English
 Cited by
1.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT,;

호남수학학술지, 2015. vol.37. 1, pp.135-147 crossref(new window)
1.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT, Honam Mathematical Journal, 2015, 37, 1, 135  crossref(new windwow)
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