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STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½ SEPARATION AXIOM
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.707-716
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.707
 Title & Authors
STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½ SEPARATION AXIOM
Han, Sang-Eon;
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 Abstract
The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff -space is a semi--space, the first part studies semi-open and semi-closed structures of the Khalimsky nD space. The second one focuses on the study of a relation between the LS-property of (, k) relative to the simple closed -curves , and its normal k-adjacency. In addition, the present paper points out that the main theorems of Boxer and Karaca`s paper [3] such as Theorems 4.4 and 4.7 of [3] cannot be new assertions. Indeed, instead they should be attributed to Theorems 4.3 and 4.5, and Example 4.6 of [10].
 Keywords
digital topology;domain theory;semi--separation axiom;semi-open;semi-closed;upper set;normal adjacency;digital product;digital covering space;
 Language
English
 Cited by
1.
UTILITY OF DIGITAL COVERING THEORY,;;

호남수학학술지, 2014. vol.36. 3, pp.695-706 crossref(new window)
2.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT,;

호남수학학술지, 2015. vol.37. 1, pp.135-147 crossref(new window)
3.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY,;;

호남수학학술지, 2015. vol.37. 4, pp.577-593 crossref(new window)
1.
UTILITY OF DIGITAL COVERING THEORY, Honam Mathematical Journal, 2014, 36, 3, 695  crossref(new windwow)
2.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY, Honam Mathematical Journal, 2015, 37, 4, 577  crossref(new windwow)
3.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT, Honam Mathematical Journal, 2015, 37, 1, 135  crossref(new windwow)
 References
1.
P. Alexandorff, Diskrete Raume, Mat. Sb. 2 (1937), 501-518.

2.
F. G. Arenas, Alexandroff Spaces, Acta Math. Univ. Comenian., (N.S.) 68 (1999), 501-518.

3.
L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences, 11(4) (2012), 161-179.

4.
V. A. Chatyrko, S. E. Han, Y. Hattori, Some remarks concerning semi-$T_{\frac{1}{2}}$ spaces, Filomat, in press.

5.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A Compendium of Continuous Lattices, Springer, Berlin-Heidelberg-New York, 1980.

6.
N. Hamllet, A correction to the paper "Semi-open sets and semi-continuity in topological spaces" by Norman Levine, Proceeding of Amer. Math. Soc. 49(2) (1975), 458-460.

7.
S. E. Han, Computer topology and its applications, Honam Math. Jour., 25(1) (2003), 153-162.

8.
S. E. Han, Non-product property of the digital fundamental group, Information Sciences 171(1-3) (2005), 73-91. crossref(new window)

9.
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. crossref(new window)

10.
S. E. Han, Cartesian product of the universal covering property, Acta Applicandae Mathematicae 108 (2009), 363-383. crossref(new window)

11.
S. E. Han, KD-(k0; k1)-homotopy equivalence and its applications, Journal of Korean Mathematical Society 47(5) (2010), 1031-1054. crossref(new window)

12.
S. E. Han, Ultra regular covering space and its automorphism group, International Journal of Applied Mathematics & Computer Science, 20(4) (2010), 699-710.

13.
E. D. Khalimsky, On topologies of generalized segments, Soviet Math. Dokl., 10 (1969), 1508-1511.

14.
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.

15.
T. Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, (1996).

16.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. crossref(new window)

17.
D. Marcus, F. Wyse et al., Solution to problem 5712, Am. Math. Monthly 77 (1970), 1119. crossref(new window)

18.
A. Rosenfeld, Arcs and curves in digital pictures, Jour. of the ACM, 20 (1973), 81-87. crossref(new window)