Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CATEGORY WHICH IS SUITABLE FOR STUDYING KHALIMSKY TOPOLOGICAL SPACES WITH DIGITAL CONNECTIVITY

  • Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2011.04.13
  • Accepted : 2011.05.23
  • Published : 2011.06.25
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Abstract

Let $X_{n,k}$ be a Khalimsky topological n dimensional subspace with digital k-connectivity. In relation to the classification of spaces $X_{n,k}$, by comparing several kinds of continuities and homeomorphisms, the paper proposes a category which is suitable for studying the spaces $X_{n,k}$.

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References

  1. P. Alexandorff, Diskrete Raume, Mat. Sb. 2 (1937) 501-518.
  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. 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
  4. S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27(1) (2005) 115-129.
  5. S.E. Han, Continuities and homeomorphisms in computer topology and their applications, Journal of the Korean Mathematical Society 45(4)(2008) 923-952. https://doi.org/10.4134/JKMS.2008.45.4.923
  6. 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
  7. 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
  8. 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. https://doi.org/10.1007/s10851-007-0061-2
  9. 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
  10. S.E. Han, N.D. Georgiou, On computer topological function space, Journal of the Korean Mathematical Society 46(4) (2009) 841-857. https://doi.org/10.4134/JKMS.2009.46.4.841
  11. S.E. Han and B.G. Park, Digital graph ($k_0,\,k_1$)-isomorphism and its applications, http://atlas-conferences.com/c/a/k/b/36.htm(2003).
  12. E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Applications, 36(1)(1990) 1-17. https://doi.org/10.1016/0166-8641(90)90031-V
  13. In-Soo Kim, S.E. Han, C.J. Yoo, The pasting property of digital continuity, Acta Applicandae Mathematicae 110 (2010) 399-408. https://doi.org/10.1007/s10440-008-9422-0
  14. T. Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.
  15. E. Melin, Extension of continuous functions in digital spaces with the Khalimsky topology, Topology and Its Applications 153(2005) 52-65. https://doi.org/10.1016/j.topol.2004.12.004
  16. A. Rosenfeld, Continuous functions on digital pictures, Pattern Recognition Letters, 4 (1986) 177-184. https://doi.org/10.1016/0167-8655(86)90017-6

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  1. COMPARISON OF CONTINUITIES IN DIGITAL TOPOLOGY vol.34, pp.3, 2012, https://doi.org/10.5831/HMJ.2012.34.3.451