Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 3 Sayı: 1, 25 - 28, 10.06.2020

Öz

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

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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Gnanachandra Prabu 0000-0001-6089-6441

S. Jafari 0000-0001-5191-9330

M.lellis Thıvagar 0000-0001-5997-5185

Yayımlanma Tarihi 10 Haziran 2020
Gönderilme Tarihi 22 Ocak 2020
Kabul Tarihi 31 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

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. Haziran 2020;3(1):25-28.
Chicago Prabu, Gnanachandra, S. Jafari, ve M.lellis Thıvagar. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications 3, sy. 1 (Haziran 2020): 25-28.
EndNote Prabu G, Jafari S, Thıvagar M (01 Haziran 2020) Topological Properties of Digital Line. Fundamental Journal of Mathematics and Applications 3 1 25–28.
IEEE G. Prabu, S. Jafari, ve M. Thıvagar, “Topological Properties of Digital Line”, Fundam. J. Math. Appl., c. 3, sy. 1, ss. 25–28, 2020.
ISNAD Prabu, Gnanachandra vd. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications 3/1 (Haziran 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 vd. “Topological Properties of Digital Line”. Fundamental Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 25-28.
Vancouver Prabu G, Jafari S, Thıvagar M. Topological Properties of Digital Line. Fundam. J. Math. Appl. 2020;3(1):25-8.

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