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ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 4,  2011, pp.617-628
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.4.617
 Title & Authors
ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM
Han, Sang-Eon; Chun, Woo-Jik;
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 Abstract
In relation to the classification of finite topological spaces the paper [17] studied various properties of finite topological spaces. Indeed, the study of future internet system can be very related to that of locally finite topological spaces with some order structures such as preorder, partial order, pretopology, Alexandroff topological structure and so forth. The paper generalizes the results from [17] so that the paper can enlarge topological and homotopic properties suggested in the category of finite topological spaces into those in the category of locally finite topological spaces including ALF spaces.
 Keywords
Locally finite topological space;ALF space;homeomorphism;digital topology;Khalimsky topology;network;
 Language
English
 Cited by
 References
1.
P. Alexandorff, Diskrete Rume, Mat. Sb. 2 (1937) 501-518.

2.
G. Birkhoff, Lattice Theory, American Mathematical Society, 1961.

3.
W. Dunham, $T{\frac{1}{2}$ spaces, Kyungpook Math. J. 17 (1977) 161-169.

4.
S.E. Han, Strong k-deformation retract and its applications, Journal of Korean Mathematical Society 44(6)(2007) 1479-1503. crossref(new window)

5.
S.E. Han, Continuities and homeomorphisms in computer topology, Journal of Korean Mathematical Society 45(4)(2008) 923-952. crossref(new window)

6.
S.E. Han, Equivalent ($k_0;\;k_1$)-covering and generalized digital lifting, Information Sciences 178(2)(2008) 550-561. crossref(new window)

7.
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)

8.
S.E. Han, Extension problem of several continuities in computer topology, Bul- letin of Korean Mathematical Society, 47(5)(2010) 915-932. crossref(new window)

9.
S.E. Han, Continuity of maps between axiomatic locally finite spaces and its ap- plications, International Journal of Computer Mathematics 88(14) (2011) 2889- 2900. crossref(new window)

10.
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.

11.
V. Kovalevsky, Axiomatic Digital Topology, Journal of Mathematical Imaging and Vision 26 (2006) 41-58. crossref(new window)

12.
V. Kovalevsky, Geometry of Locally Finite Spaces, Monograph, Berlin (2008).

13.
V. Kovalevsky, Sang-Eon Han, Product and hereditary property of space set topological structure, Transactions of AMS, submitted.

14.
A. Rosenfeld, Connectivity in digital pictures, Journal of the ACM 17 (1970) 146-160. crossref(new window)

15.
H. Seifert and W. Threlfall, A Textbook of Topology, Academic Press, 1980.

16.
J. Stillwell, Classical Topology and Combinatorial Group Theory, Springer (1995).

17.
R.E.Stong, Finite topological spaces, Transactions of AMS 123 (1966) 325-340. crossref(new window)