Research Article
BibTex RIS Cite

Year 2020, Volume: 3 Issue: 1, 25 - 28, 10.06.2020

Gnanachandra Prabu , S. Jafari , M.lellis Thıvagar

Abstract

References

  • [1] A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979), 621 - 630.
  • [2] A. Rosenfeld, Digital straight line segments, IEEE Trans. Computers, 23 (1994), 1264 - 1269.
  • [3] A. Rosenfeld, Digital Picture Analysis, Springer, Berlin, 1976.
  • [4] A. Rosenfeld, A. C. Kak, Digital Picture Processing, Academic Press, New York, 1976.
  • [5] E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Top. Appl., 36 (1990), 1 - 17.
  • [6] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1) (1963), 36 - 41.
  • [7] P. Thangavelu, K. C. Rao, p-sets in topological spaces, Bull. Pure Appl. Math., 21E(2) (2002), 341 - 355.
  • [8] T. Y. Kong, R. Kopperman, A topological approach to digital topology, Amer. Math. Monthly, 98 (10), (1991), 901 - 907.
  • [9] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2) (1970), 89 - 96.
  • [10] S. N. Maheswari, R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelle Ser., 89 III (1975), 395 - 402.
  • [11] C. H. Dorsett, Semi-T2, Semi-R1 and Semi-R0 topological spaces, Ann. Soc. Sci. Bruxelle Ser., (I,92) (1978), 143 - 150.
  • [12] S. Willard, General Topology, Addison Wesley, 1970.
  • [13] J. L. Kelly, General Topology, Princeton, NJ.D.Van Nastrand, 1955.
  • [14] P. Alexandroff, Diskrete Raume, Mat. Sbornik, 2 (1937), 507 - 519.
  • [15] N. Levine, On the community of the closure and interior operators in topological spaces, Amer. Math. Monthly, 68 (1961), 474 - 477.

Topological Properties of Digital Line

Year 2020, Volume: 3 Issue: 1, 25 - 28, 10.06.2020

Gnanachandra Prabu , S. Jafari , M.lellis Thıvagar

Abstract

The main purpose of Digital topology is the study of topological properties of discrete objects which are obtained digitizing continuous objects. Digital topology plays a very important role in computer vision, image processing and computer graphics. The ultimate aim of this article is to analyze the behavior of various general topological concepts in the Khalimsky topology. In this article, we provide some results and examples of topology on $ \mathbb{Z}$, the set of all integers. Also, we explain the concepts of digital line and digital intervals with illustrative counterexamples.

Keywords

Digital interval Digital topology Khalimsky line

References

  • [1] A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979), 621 - 630.
  • [2] A. Rosenfeld, Digital straight line segments, IEEE Trans. Computers, 23 (1994), 1264 - 1269.
  • [3] A. Rosenfeld, Digital Picture Analysis, Springer, Berlin, 1976.
  • [4] A. Rosenfeld, A. C. Kak, Digital Picture Processing, Academic Press, New York, 1976.
  • [5] E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Top. Appl., 36 (1990), 1 - 17.
  • [6] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1) (1963), 36 - 41.
  • [7] P. Thangavelu, K. C. Rao, p-sets in topological spaces, Bull. Pure Appl. Math., 21E(2) (2002), 341 - 355.
  • [8] T. Y. Kong, R. Kopperman, A topological approach to digital topology, Amer. Math. Monthly, 98 (10), (1991), 901 - 907.
  • [9] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2) (1970), 89 - 96.
  • [10] S. N. Maheswari, R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelle Ser., 89 III (1975), 395 - 402.
  • [11] C. H. Dorsett, Semi-T2, Semi-R1 and Semi-R0 topological spaces, Ann. Soc. Sci. Bruxelle Ser., (I,92) (1978), 143 - 150.
  • [12] S. Willard, General Topology, Addison Wesley, 1970.
  • [13] J. L. Kelly, General Topology, Princeton, NJ.D.Van Nastrand, 1955.
  • [14] P. Alexandroff, Diskrete Raume, Mat. Sbornik, 2 (1937), 507 - 519.
  • [15] N. Levine, On the community of the closure and interior operators in topological spaces, Amer. Math. Monthly, 68 (1961), 474 - 477.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gnanachandra Prabu 0000-0001-6089-6441

S. Jafari 0000-0001-5191-9330

M.lellis Thıvagar 0000-0001-5997-5185

Publication Date June 10, 2020
Submission Date January 22, 2020
Acceptance Date January 31, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Prabu, G., Jafari, S., & Thıvagar, M. (2020). Topological Properties of Digital Line. Fundamental Journal of Mathematics and Applications, 3(1), 25-28.
AMA Prabu G, Jafari S, Thıvagar M. Topological Properties of Digital Line. Fundam. J. Math. Appl. June 2020;3(1):25-28.
Chicago Prabu, Gnanachandra, S. Jafari, and M.lellis Thıvagar. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications 3, no. 1 (June 2020): 25-28.
EndNote Prabu G, Jafari S, Thıvagar M (June 1, 2020) Topological Properties of Digital Line. Fundamental Journal of Mathematics and Applications 3 1 25–28.
IEEE G. Prabu, S. Jafari, and M. Thıvagar, “Topological Properties of Digital Line”, Fundam. J. Math. Appl., vol. 3, no. 1, pp. 25–28, 2020.
ISNAD Prabu, Gnanachandra et al. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications 3/1 (June 2020), 25-28.
JAMA Prabu G, Jafari S, Thıvagar M. Topological Properties of Digital Line. Fundam. J. Math. Appl. 2020;3:25–28.
MLA Prabu, Gnanachandra et al. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications, vol. 3, no. 1, 2020, pp. 25-28.
Vancouver Prabu G, Jafari S, Thıvagar M. Topological Properties of Digital Line. Fundam. J. Math. Appl. 2020;3(1):25-8.
 Download Cover Image

Creative Commons License
The published articles in Fundamental Journal of Mathematics and Applications are licensed under a