Abstract

This paper deals with some separation properties of the digital line, semi-regularity, semi-normality, Tb separation and Tb separation of the digital line.

References

• M. E. Abd El-Monsef, S. Rose Mary and M. Lellis Thivagar, 2007, -closed sets in topological spaces, Assiut Univ. J. of Mathematics and Computer Science,36(1)43-51.
• S. P. Arya and T. Nour, 1990, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. , 21(8), 717-719.
• P. Bhattacharya and B. K. Lahiri, 1987, Semi-generalised closed sets in topology, Indian J. Math. , 29, 375-382.
• J. Dontchev and M. Ganster, 1996, On generalized closed sets and T3/4 -spaces, Mem. Fac. Sci. Kochi Univ. (math),17,15-42.
• C. Dorsett, 1982, Semi-regular spaces, Soochow J. Math. 8, 45-53.
• C. Dorsett, 1985, Semi-normal spaces, Kyungpook Math. J25, 173-180.
• W. Dunham, 1977, T1/2-spaces, Kyungpook Math. J. 17,161-169.
• M. Fujimoto, S. Takigava, J. Dontchev, T. Noiri and H. Maki, 2006, The topological structures and groups of digital n-spaces, Kochi J. Math. , 1, 31-55.
• T. Fukutake, P. Sundaram and M. Sheik John, 2002, -ciosed sets, -open sets and -continuity in bitopological spaces, Bull. Fukuoka Univ. Ed. Part III, 51,1-9.
• E. D. Khalimsky, 1970, Applications of connected ordered topological spaces in topology, Conference of math. departments of Povolsia.
• E. D. Khalimsky, 1987, Topologicals structures in computer sciences, J . Appl. Math. , Simulation, 1(1) , 25-40.
• E. D. Khalimsky, R. Kopperman and P. R. Meyer, 1990, Computer graphics and connected topologies on finite ordered sets, Topology Appl. , 36,1-17.
• T. Y. Kong, R. Kopperman and P. R. Meyer, 1991, A topologicai approach to digital topology, Amer. Math. Monthly, 98, 901- 917.
• V. Kovalevsky and R. Kopperman, 1994, Some topology-based image processing algorithms, Annals of the New York Academy of Sciences, Papers on General Topology and its Applications, 728, 174-182.
• N. Levine, 1963, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70, 36-41.
• N. Levine, 1970, Generalised closed sets in topology, Rend. circ. Mat. Palermo, 19, 89-96.
• S. Maheshwari and R. Prasada, 1978, On s-normai spaces, Bull. Math. Soc. Sci. R. S. Roumanie, 22(70) ( 1), 27-29.
• A. S. Mashhour, M. E. Abd El-Monsef and S. N. El Deeb, 1982, On pre continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt. , 53, 47-53.
• H. Maki, R. Devi and K. Balachandran, 1994, Associated topologies of generalized -closed sets and -generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 15, 51-63.
• S. I. Nada, 2004, Semi-open and semi-closed sets in digital toprological spaces, Commun. Fac. Sci. Uniu. Ank. Series A1, 53(1), 1-6.
• O. Njastad, 1965, On some classes of nearly open sets, Pacific J. Math. 15, 961- 970.
• M. Sheik John, 2000, A study on generalizations of closed sets and continuous maps in topoiogical spaces, Ph. D. Thesis, Bharathiar University, Coimbatore, India.
• P. Sundaram and M. Sheik John, 1995, Weakly closed sets weak continuous maps in topological spaces, Proc. 82 nd Indian Sci. Cong. Calcutta, 49.
• P. Sundaram ancl M. Sheik John, 2000, On -closed sets in topology, Acta ciencia Indica, 26M (4), 389-392.