Browse > Article
http://dx.doi.org/10.5831/HMJ.2011.33.4.575

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)
Publication Information
Honam Mathematical Journal / v.33, no.4, 2011 , pp. 575-589 More about this Journal
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 $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.
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;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 F. Wyse and D. Marcus et al., Solution to problem 5712, Am. Math. Monthly 77(1970) 1119.   DOI   ScienceOn
2 P. Alexandorff, Diskrete Raume, Mat. Sb. 2 (1937) 501-518.
3 S.E. Han, Strong k-deformation retract and its applications, Journal of the Ko- rean Mathematical Society 44(6)(2007) 1479-1503.   과학기술학회마을   DOI   ScienceOn
4 S.E. Han, Continuities and homeomorphisms in computer topology and their applications, Journal of the Korean Mathematical Society 45(4)(2008) 923-952.   과학기술학회마을   DOI   ScienceOn
5 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.   DOI
6 E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl., 36(1)(1990) 1-17.   DOI   ScienceOn
7 H. Kofler, The topological consistence of path connectedness in regular and ir- regular structures, LNCS 1451(1998) 445-452.
8 T. Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Pro- cessing, Elsevier Science, Amsterdam, 1996.
9 P. Ptak, H. Ko er and W. Kropatsch, Digital topologies revisited: An approach based on the topological point-neighborhood, LNCS 1347(1997) 151-159.
10 A. Rosenfeld, Digital topology, Am. Math. Mon. 86(1979) 76-87.