Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOME PROPERTIES OF LATTICE-BASED K- AND M-MAPS

  • Han, Sang-Eon (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Lee, Sik (Department of Mathematics Education, Chonnam National University)
  • Received : 2016.07.08
  • Accepted : 2016.09.05
  • Published : 2016.09.25
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Abstract

The recent papers [7, 12] developed two maps named by an LA- [7] and an LMA-map [12]. The present paper studies their properties and further, develops generalized versions of an LA- and an LMA-map, which makes the LA- [7] and the LMA-map [12] improved.

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References

  1. P. Alexandorff, Diskrete Raume, Mat. Sb. 2 (1937) 501-518.
  2. V. A. Chatyrko, S. E. Han, Y. Hattori, Some remarks concerning semi-$T_{\frac{1}{2}}$ spaces, Filomat, 28(1) (2014) 21-25. https://doi.org/10.2298/FIL1401021C
  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, 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
  6. S.-E. Han, KD-$(k_0,\;k_1)$-homotopy equivalence and its applications, J. Korean Math. Soc. 47 (2010) 1031-1054. https://doi.org/10.4134/JKMS.2010.47.5.1031
  7. S.-E. Han, A digitization method of the Euclidean nD space associated with the Khalimsky adjacency structure, Computational and Applied Mathematics (2015), DOI 10.1007/s40314-015-0223-6 (in press).
  8. S.-E. Han, Generalilzation of continuity of maps and homeomorphism for studying 2D digital topological spaces and their applications, Topology and its applications, 196 (2015) 468-482. https://doi.org/10.1016/j.topol.2015.05.024
  9. S.-E. Han, A link between the FPP for Euclidean spaces and the FPP for their Khalimsky-topologically digitized spaces (2016), submitted.
  10. S.-E. Han and Woo-Jik Chun, Classification of spaces in terms of both a dizitization and a Marcus-Wyse topological structure, Honam Math. J. 33(4)(2011) 575-589. https://doi.org/10.5831/HMJ.2011.33.4.575
  11. S.-E. Han, A. Sostak, A compression of digital images derived from a Khalimsky topological structure, Computational and Applied Mathematics 32 (2013) 521-536. https://doi.org/10.1007/s40314-013-0034-6
  12. S.-E. Han and Wei Yao, An MA-Digitization of Hausdorff spaces by using a connectedness graph of the Marcus-Wyse topology, Discrete Applies Mathematics, 201 (2016) 358-371.
  13. 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/35.htm (2003).
  14. J.M. Kang, S.-E. Han and K.C. Min, Digitizations associated with several types of digital topological approaches, Computational and Applied Mathematics, DOI 10.1007/s40314-015-0245-0 (in press) (2015).
  15. E.D. Khalimsky, Applications of connected ordered topological spaces in topology, Conference of Math. Department of Provoia, (1970).
  16. E. Khalimsky, R. Kopperman, P.R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology and Its Applications, 36(1) (1991) 1-17. https://doi.org/10.1016/0166-8641(90)90031-V
  17. T. Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.
  18. V. Kovalevsky, Axiomatic Digital Topology, Journal of Mathematical Imaging and Vision 26 (2006) 41-58. https://doi.org/10.1007/s10851-006-7453-6
  19. A. Rosenfeld, Digital topology, Am. Math. Mon. 86 (1979) 76-87.
  20. A. Rosenfeld, Continuous functions on digital pictures, Pattern Recognition Letters, 4 (1986) 177-184. https://doi.org/10.1016/0167-8655(86)90017-6
  21. F. Wyse and D. Marcus et al., Solution to problem 5712, Amer. Math. Monthly 77(1970) 1119. https://doi.org/10.2307/2316121

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  1. Homotopic properties of an MA -digitization of 2D Euclidean spaces 2017, https://doi.org/10.1016/j.jcss.2017.07.003