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2010 | 20 | 4 | 699-710
Tytuł artykułu

Ultra regular covering space and its automorphism group

Autorzy
Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
20
Numer
4
Strony
699-710
Opis fizyczny
Daty
wydano
2010
otrzymano
2010-01-10
poprawiono
2010-05-10
Twórcy
autor
  • Institute of Pure and Applied Mathematics, Faculty of Liberal Education, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, South Korea
Bibliografia
  • Boxer, L. (1999). A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10(1): 51-62.
  • Boxer, L. (2006). Digital products, wedge, and covering spaces, Journal of Mathematical Imaging and Vision 25(2): 159-171.
  • 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.
  • Han, S.E. (2006a). Connected sum of digital closed surfaces, Information Sciences 176(3): 332-348.
  • Han, S.E. (2006b). Discrete Homotopy of a Closed k-Surface, Lecture Notes in Computer Science, Vol. 4040, Springer-Verlag, Berlin, pp. 214-225.
  • 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.
  • Han, S.E. (2007a). Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44(6): 1479-1503.
  • Han, S.E. (2007b). The k-fundamental group of a closed ksurface, Information Sciences 177(18): 3731-3748.
  • Han, S.E. (2008a). Comparison among digital fundamental groups and its applications, Information Sciences 178(8): 2091-2104.
  • Han, S.E. (2008b). Equivalent (k₀,k₁)-covering and generalized digital lifting, Information Sciences 178(2): 550-561.
  • Han, S.E. (2008c). Map preserving local properties of a digital image, Acta Applicandae Mathematicae 104(2): 177-190.
  • Han, S.E. (2008d). The k-homotopic thinning and a torus-like digital image in Zn , Journal of Mathematical Imaging and Vision 31(1): 1-16.
  • Han, S.E. (2009a). Cartesian product of the universal covering property, Acta Applicandae Mathematicae 108(2): 363-383.
  • Han, S.E. (2009b). Regural covering space in digital covering theory and its applications, Honam Mathematical Journal 31(3): 279-292.
  • Han, S.E. (2009c). Remark on a generalized universal covering space, Honam Mathematical Journal 31(3): 267-278.
  • Han, S.E. (2010a). Existence problem of a generalized universal covering space, Acta Applicandae Mathematicae 109(3): 805-827.
  • Han, S.E. (2010b). Multiplicative property of the digital fundamental group, Acta Applicandae Mathematicae 110(2): 921-944.
  • Han, S.E. (2010c). KD-(k₀,k₁)-homotopy equivalence and its applications, Journal of the Korean Mathematical Society 47(5): 1031-1054.
  • Han, S.E. (2010d). Properties of a digital covering space and discrete Deck's transformation group, The IMA Journal of Applied Mathematics, (submitted).
  • Khalimsky, E. (1987). Motion, deformation, and homotopy in finite spaces, Proceedings of IEEE International Conferences on Systems, Man, and Cybernetics, pp. 227-234.
  • Kim I.-S., and Han, S.E. (2008). Digital covering theory and its applications, Honam Mathematical Journal 30(4): 589-602.
  • Kong, T.Y. and Rosenfeld, A. (1996). Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam.
  • Malgouyres, R. and Lenoir, A. (2000). Topology preservation within digital surfaces, Graphical Models 62(2): 71-84.
  • Massey, W.S. (1977). Algebraic Topology, Springer-Verlag, New York, NY.
  • Rosenfeld, A. (1979). Digital topology, American Mathematical Monthly 86: 76-87.
  • Rosenfeld, A. and Klette, R. (2003). Digital geometry, Information Sciences 148: 123-127.
  • Spanier, E.H. (1966). Algebraic Topology, McGraw-Hill Inc., New York, NY.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i4p699bwm
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