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International Journal Of Chemistry, Mathematics And Physics(IJCMP)

The Khalimsky Line Topology- Countability and Connectedness

S.A Bhuiyan


International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-6,Issue-4, July - August 2022, Pages 1-4 , 10.22161/ijcmp.6.4.1

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Article Info: Received: 25 Jun 2022; Received in revised form: 15 Jul 2022; Accepted: 22 Jul 2022; Available online: 27 Jul 2022

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The concepts of connectedness and countability in digital image processing are used for establishing boundaries of objects and components of regions in an image. The purpose of this paper is to investigate some notions of connectedness and countability of Khalimsky line topology.

Countability, Khalimsky line, Khalimsky arc connected space.

[1] A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979), 621 – 630
[2] S.Mishra and M.Aaliya, Application of Topology in Science and Technology, International Journal of Research and Analytical Reciews,5(2018)101-104.
[3] Kopperman, R. (1994). The Khalimsky Line as a Foundation for Digital Topology. In: O, YL., Toet, A., Foster, D., Heijmans, H.J.A.M., Meer, P. (eds) Shape in Picture. NATO ASI Series, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03039-4_2 .
[4] S. Jafari and A. Selvakumar, On Some Sets in Digital Topology, Poincare Journal of Analysis & ApplicationsVol. 8, No. 1(I) (2021), DOI: 10.33786/pjaa.2021.v08i01(i).001.
[5] Seymour Lipschutz, General Topology, Schaum’s Outline Series.
[6] Abd El-Monem M. Kozae1 and El-Sayed A. Abo-Tabl, On Digital Line and Operations, General Letters in Mathematics Vol. 4, No. 3, June 2018, pp.107-113, https://doi.org/10.31559/glm2018.4.
[7] Anne Kurie K., M. S. Samuel,Continuity in Digital Spaces with The Khalimsny
Topology,International Journal of MathematicsTrends and Technology 53(2018),65-67
[8] G.Gutierres,What is First Countable Space?, Topology and Its Applications,153(2006)3420-3429. doi:10.1016/j.topol.2006.03.003
[9] K. Annie Kurien1 and M. S. Samuel, Connectedness in Digital Spaces with the Khalimsky
Topology, Int. J. Math. And Appl., 6(1–D)(2018), 773–774.
[10] James F. Peters, Topology of Digital Images, Springer-Verleg Berlin Heidelkberg,2014.