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CLASSIFICATION OF SPACES IN TERMS OF BOTH A DIGITIZATION AND A MARCUS WYSE TOPOLOGICAL STRUCTURE
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 4,  2011, pp.575-589
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.4.575
 Title & Authors
CLASSIFICATION OF SPACES IN TERMS OF BOTH A DIGITIZATION AND A MARCUS WYSE TOPOLOGICAL STRUCTURE
Han, Sang-Eon; Chun, Woo-Jik;
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 Abstract
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 in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.
 Keywords
Marcus Wyse topology;digitization;Marcus Wyse connectedness;Marcus Wyse continuous map;Marcus Wyse homeomorphism;lattice based Marcus Wyse continuous map;lattice based Marcus Wyse homeomorphism;
 Language
English
 Cited by
1.
SOME PROPERTIES OF LATTICE-BASED K- AND M-MAPS, Honam Mathematical Journal, 2016, 38, 3, 625  crossref(new windwow)
2.
Generalizations of continuity of maps and homeomorphisms for studying 2D digital topological spaces and their applications, Topology and its Applications, 2015, 196, 468  crossref(new windwow)
3.
Digitizations associated with several types of digital topological approaches, Computational and Applied Mathematics, 2015  crossref(new windwow)
4.
Homotopy based on Marcus–Wyse topology and its applications, Topology and its Applications, 2016, 201, 358  crossref(new windwow)
5.
An MA-digitization of Hausdorff spaces by using a connectedness graph of the Marcus–Wyse topology, Discrete Applied Mathematics, 2016  crossref(new windwow)
 References
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. crossref(new window)

3.
S.E. Han, Continuities and homeomorphisms in computer topology and their applications, Journal of the Korean Mathematical Society 45(4)(2008) 923-952. crossref(new window)

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. crossref(new window)

5.
E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl., 36(1)(1990) 1-17. crossref(new window)

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. crossref(new window)