JOURNAL BROWSE
Search
Advanced SearchSearch Tips
REGULAR COVERING SPACE IN DIGITAL COVERING THEORY AND ITS APPLICATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 31, Issue 3,  2009, pp.279-292
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2009.31.3.279
 Title & Authors
REGULAR COVERING SPACE IN DIGITAL COVERING THEORY AND ITS APPLICATIONS
Han, Sang-Eon;
  PDF(new window)
 Abstract
As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.
 Keywords
digital space;digital isomorphism;strong k-deformation retract;regular covering space;digital covering space;simply k-connected;discrete Deck's transformation group;automorphism group;
 Language
English
 Cited by
1.
PROPERTIES OF A GENERALIZED UNIVERSAL COVERING SPACE OVER A DIGITAL WEDGE,;

호남수학학술지, 2010. vol.32. 3, pp.375-387 crossref(new window)
2.
REMARKS ON DIGITAL PRODUCTS WITH NORMAL ADJACENCY RELATIONS,;;

호남수학학술지, 2013. vol.35. 3, pp.515-524 crossref(new window)
1.
PROPERTIES OF A GENERALIZED UNIVERSAL COVERING SPACE OVER A DIGITAL WEDGE, Honam Mathematical Journal, 2010, 32, 3, 375  crossref(new windwow)
2.
REMARKS ON DIGITAL PRODUCTS WITH NORMAL ADJACENCY RELATIONS, Honam Mathematical Journal, 2013, 35, 3, 515  crossref(new windwow)
 References
1.
L. Boxer , A classical construction for the digital fundamental group, Jour. of Mathematical Imaging and Vision, 10(1999) 51-62. crossref(new window)

2.
L. Boxer, Digital Product s, Wedge: and Covering Spaces, Jour. of Mathematical Imaging and Vision 25(2006) 159-171. crossref(new window)

3.
L. Boxer and I. Karaca, The classification of digital covering spaces, Jour. of Mathematical Imaging and Vision 32(2008) 23-29. crossref(new window)

4.
S.E. Han, Computer topology and its applications, Honam Math. Jour. 25(1)(2003) 153-162.

5.
S.E. Han, Algorithm for discriminating digital images w.r.t. a digital ($k_0$, $k_1$)-homeomorphism, Jour. of Applied Mathematics and Computing 18(1-2)(2005) 505-512.

6.
S.E. Han, Digital coverings and their applications, Jour. of Applied Mathematics and Computing 18 (1-2)(2005) 487-495.

7.
S.E. Han, Non-product property of t he 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, Connected sum of digital closed surfaces, Information Sciences 176(3)(2006)332-348. crossref(new window)

10.
S.E. Han, Discrete Homotopy of a Closed k-Surface. LNCS 4040. Springer-Verlag, Berlin, pp.214-225 (2006). crossref(new window)

11.
S.E. Han, Minimal simple closed k-surfaces and a topological preservation of 3D surfaces, Information Sciences 176(2)(2006) 120-134. crossref(new window)

12.
S.E. Han, The fundamental group of a closed k-surface, Information Sciences 177(18)(2007) 3731-3748. crossref(new window)

13.
S.E. Han, Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44 (6)(2007) 1479-1503. crossref(new window)

14.
S.E. Han, Comparison among digital fundamental groups and its applications, Information Science 178(2008) 2091-2104. crossref(new window)

15.
S.E. Han, Continuities and homeomorphisms in computer topology, Journal of the Korean Mathematical Society 45 (4)(2008) 923-952. crossref(new window)

16.
S.E. Han, Equivalent ($k_0$, $k_1$)-covering and generalized digital lifting, Information Sciences 178(2)(2008)550-561. crossref(new window)

17.
S.E. Han, Map preserving local properties of a digital image, Acta Applicandae Mathematicae 104 (2) (2008) 177-190. crossref(new window)

18.
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)

19.
S.E. Han, Cartesian product of the universal covering property, Acta Applicandae Mathematicae (2009) doi 10.1007/s 10440-008-9316-1, Online first publication. crossref(new window)

20.
S.E. Han, Existence problem of a generalized universal covering space, Acta Applicandae Mathematicae(2009) doi 10.1007/s 10440-008-9347-7, Online first publication. crossref(new window)

21.
S.E. Han, Multiplicative property of the digital fundamental group. (2009) doi 10.1007/s 10440-009-9486-5, Online first publication. crossref(new window)

22.
S.E. Han, KD-$k_0$, $k_1$)-homotopy equivalence and its applications, Journal of Korean Mathematical Society, to appear.

23.
S.E. Han, Automorphism group of a cartes ian product of digital coverings, Annals of Mathematics, submitted.

24.
S.E. Han, N.D. Georgiou. On computer topological function space Journal of the Korean Mathematical Society 46(4) 841-857 (2009). crossref(new window)

25.
E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conferences on Systems, Man, and Cybernetics(1987) 227-234.

26.
In-Soo Kim, S.E. Han, Digital covering therory and its applications, Honam Mathematical Journal 30(4) (2008) 589-602. crossref(new window)

27.
In-Soo Kim, S.E. Han, C.J. Yoo, The pasting property of digital continuity. Acta Applicandae Mathematicae (2009), doi 10.1007/s 10440-008-9422-0, Online first publication. crossref(new window)

28.
T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, (1996).

29.
W.S. Massey, Algebraic Tnpology, Springer-Verlag, New York, 1977.

30.
A. Rosenfeld, Digital topology, Am. Math. Mon. 86(1979) 76-87.

31.
A. Rosenfeld and R. Klette, Digital geometry. Information Sciences 148(2003)123-127. crossref(new window)

32.
E.H. Spanier, Algebraic Topology, McGraw-Hill Inc., New York, 1966.