Ultra regular covering space and its automorphism group

• Autorzy: Sang-Eon Han
• Języki publikacji: EN

Abstrakty

EN

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

Słowa kluczowe

EN

digital image; digital isomorphism; (ultra) regular covering space; digital covering space; simply k-connected; Deck's discrete transformation group; compatible adjacency; digital wedge; automorphism group

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 4
• Strony: 699-710

Daty

wydano

2010

otrzymano

2010-01-10

poprawiono

2010-05-10

Twórcy

autor

Sang-Eon Han

• Institute of Pure and Applied Mathematics, Faculty of Liberal Education, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, South Korea

Bibliografia

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• Boxer, L. and Karaca, I. (2008). The classification of digital covering spaces, Journal of Mathematical Imaging and Vision 32(1): 23-29.
• Han, S.E. (2003). Computer topology and its applications, Honam Mathematical Journal 25(1): 153-162.
• Han, S.E. (2005a). Algorithm for discriminating digital images w.r.t. a digital (k₀,k₁)-homeomorphism, Journal of Applied Mathematics and Computing 18(1-2): 505-512.
• Han, S.E. (2005b). Digital coverings and their applications, Journal of Applied Mathematics and Computing 18(1-2): 487-495.
• Han, S.E. (2005c). Non-product property of the digital fundamental group, Information Sciences 171 (1-3): 73-91.
• Han, S.E. (2005d). On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27(1): 115-129.
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• Han, S.E. (2006c). Erratum to 'Non-product property of the digital fundamental group', Information Sciences 176(1): 215-216.
• Han, S.E. (2006d). Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Information Sciences 176(2): 120-134.
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Identyfikatory

DOI

10.2478/v10006-010-0053-z