Yıl 2020,
Cilt: 3 Sayı: 1, 25 - 28, 10.06.2020
Gnanachandra Prabu
,
S. Jafari
,
M.lellis Thıvagar
Kaynakça
- [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
Yıl 2020,
Cilt: 3 Sayı: 1, 25 - 28, 10.06.2020
Gnanachandra Prabu
,
S. Jafari
,
M.lellis Thıvagar
Öz
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.
Kaynakça
- [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.