Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PROPERTIES OF A GENERALIZED UNIVERSAL COVERING SPACE OVER A DIGITAL WEDGE

  • Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2010.07.06
  • Accepted : 2010.08.07
  • Published : 2010.09.25
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Abstract

The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

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References

  1. R. Ayala, E. Dominguez, A.R. Frances, and A. Quintero, Homotopy in digital spaces, Discrete Applied Math, 125(1) (2003) 3-24. https://doi.org/10.1016/S0166-218X(02)00221-4
  2. L. Boxer, A classical construction for the digital fundamental group, Jour. of Mathematical Imaging and Vision, 10(1999) 51-62. https://doi.org/10.1023/A:1008370600456
  3. L. Boxer, Digital Products, Wedge; and Covering Spaces, Jour. of Mathematical Imaging and Vision 25(2006) 159-171. https://doi.org/10.1007/s10851-006-9698-5
  4. 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.
  5. S.E. Han, Digital coverings and their applications, Jour. of Applied Mathematics and Computing 18(1-2)(2005) 487-495.
  6. S.E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (1-3)(2005) 73-91. https://doi.org/10.1016/j.ins.2004.03.018
  7. S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27 (1)(2005) 115-129.
  8. S.E. Han, Erratum to "Non-product property of the digital fundamental group", Information Sciences 176(1)(2006) 215-216. https://doi.org/10.1016/j.ins.2005.03.014
  9. S.E. Han, Discrete Homotopy of a Closed k-Surface, LNCS 4040, Springer-Verlag, Berlin, pp.214-225 (2006).
  10. S.E. Han, Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Information Sciences 176(2)(2006) 120-134. https://doi.org/10.1016/j.ins.2005.01.002
  11. S.E. Han, Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44(6)(2007) 1479-1503. https://doi.org/10.4134/JKMS.2007.44.6.1479
  12. S.E. Han, Comparison among digital fundamental groups and its applications. Information Sciences 178(2008) 2091-2104. https://doi.org/10.1016/j.ins.2007.11.030
  13. S.E. Han, Equivalent ($k_0, k_1$)-covering and generalized digital lifting, Information Sciences 178(2)(2008)550-561. https://doi.org/10.1016/j.ins.2007.02.004
  14. S.E. Han, Map preserving local properties of a digital image Acta Applicandae Mathematicae 104(2) (2008) 177-190- https://doi.org/10.1007/s10440-008-9250-2
  15. S.E. Han, The k-homotopic thinning and a torus-like digital image in Z", Journal of Mathematical Imaging and Vision 31 (1)(2008) 1-16. https://doi.org/10.1007/s10851-007-0061-2
  16. S.E. Han, Cartesian product of the universal covering property Acta Applicandae Mathematicae 108 (2009) 363-383. https://doi.org/10.1007/s10440-008-9316-1
  17. S.E. Han, Regural covering space in digital covering theory and its applications. Honam Mathematical Journal 31(3) (2009) 279-292. https://doi.org/10.5831/HMJ.2009.31.3.279
  18. S.E. Han, Remark on a generalized universal covering space, Honam Mathematical Jour 31(3) (2009) 267-278. https://doi.org/10.5831/HMJ.2009.31.3.267
  19. S.E. Han, Existence problem of a generalized universal covering space, Acta Applicandae Mathematicae 109(3) (2010) 805-827. https://doi.org/10.1007/s10440-008-9347-7
  20. S.E. Han, KD-($k_0, k_1$)-homotopy equivalence and its applications Journal of Korean Mathematical Society 47(5) (2010) 1031-1054. https://doi.org/10.4134/JKMS.2010.47.5.1031
  21. S.E. Han, Ultra regular covering space and its automorphism group International Journal of Applied Mathematics Computer Science, accepted.
  22. S.E. Han, Properties of a digital covering spaces and discrete Deck's transformation group Acta Applicandae Mathematicae, submitted
  23. E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conferences on Systems, Man, and Cybernetics(1987) 227-234.
  24. T.Y. Kong, A digital fundamental group Computers and Graphics 13 (1989) 159-166. https://doi.org/10.1016/0097-8493(89)90058-7
  25. T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, (1996).
  26. W.S. Massey, Algebraic Topology, Springer-Verlag, New York, 1977.
  27. A. Rosenfeld, Digital topology, Am. Math. Mon. 86(1979) 76-87.
  28. E.H. Spanier, Algebraic Topology, McGraw-Hill Inc., New York, 1966.