호남수학학술지 (Honam Mathematical Journal)

  • 제33권4호
  • /
  • Pages.575-589
  • /
  • 2011
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

CLASSIFICATION OF SPACES IN TERMS OF BOTH A DIGITIZATION AND A MARCUS WYSE TOPOLOGICAL STRUCTURE

  • Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Chun, Woo-Jik (Future Internet Architecture Research Team, Internet Service Research Department, Internet Research Laboratory, ETRI)
  • 투고 : 2011.10.05
  • 심사 : 2011.10.24
  • 발행 : 2011.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.

키워드

참고문헌

  1. P. Alexandorff, Diskrete Raume, Mat. Sb. 2 (1937) 501-518.
  2. S.E. Han, Strong k-deformation retract and its applications, Journal of the Ko- rean Mathematical Society 44(6)(2007) 1479-1503. https://doi.org/10.4134/JKMS.2007.44.6.1479
  3. 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
  4. S.E. Han, The k-homotopic thinning and a torus-like digital image in $\mathbf{Z}^n$, Journal of Mathematical Imaging and Vision 31 (1)(2008) 1-16. https://doi.org/10.1007/s10851-007-0061-2
  5. E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl., 36(1)(1990) 1-17. https://doi.org/10.1016/0166-8641(90)90031-V
  6. H. Kofler, The topological consistence of path connectedness in regular and ir- regular structures, LNCS 1451(1998) 445-452.
  7. T. Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Pro- cessing, Elsevier Science, Amsterdam, 1996.
  8. P. Ptak, H. Ko er and W. Kropatsch, Digital topologies revisited: An approach based on the topological point-neighborhood, LNCS 1347(1997) 151-159.
  9. A. Rosenfeld, Digital topology, Am. Math. Mon. 86(1979) 76-87.
  10. F. Wyse and D. Marcus et al., Solution to problem 5712, Am. Math. Monthly 77(1970) 1119. https://doi.org/10.2307/2316121

피인용 문헌

  1. The fixed point property of an M -retract and its applications vol.230, 2017, https://doi.org/10.1016/j.topol.2017.08.026
  2. Digitizations associated with several types of digital topological approaches vol.36, pp.1, 2017, https://doi.org/10.1007/s40314-015-0245-0
  3. An MA-digitization of Hausdorff spaces by using a connectedness graph of the Marcus–Wyse topology vol.216, 2017, https://doi.org/10.1016/j.dam.2016.01.007
  4. Homotopy based on Marcus–Wyse topology and its applications vol.201, 2016, https://doi.org/10.1016/j.topol.2015.12.047
  5. Generalizations of continuity of maps and homeomorphisms for studying 2D digital topological spaces and their applications vol.196, 2015, https://doi.org/10.1016/j.topol.2015.05.024
  6. SOME PROPERTIES OF LATTICE-BASED K- AND M-MAPS vol.38, pp.3, 2016, https://doi.org/10.5831/HMJ.2016.38.3.625
  7. Homotopic properties of an MA -digitization of 2D Euclidean spaces 2017, https://doi.org/10.1016/j.jcss.2017.07.003