Contra ( i,j ) -Sc- Continuous Function


Hardi N. Aziz

Sulaimani University, Faculty of Science and Science Education, School of Science Education, Sulaimani, Kurdistan Region – Iraq



Abstract
In this paper, a new type of continuity in Bitopological spaces has been introduced,
namely Contra
( ) continuity. Also, the relationship between this type of
continuity and several other known type of continuity has been dealt with.
 

Key Words: (i , j )Sc - open set, Contra semi – continuous, Contra ( ) continuous 



References
[1] Stone M. H., “Applications of the theory of Boolean rings to topology”, Trans. Amer. Math.
Soc., (41), 375 – 481, (1937).

[2] Sharma J. N., Chauhan J. P.,” Topology (general and Algebraic)”, Krishna Prakashsan Media,
India, 2011.
[3] Levine N., “Semi–open sets and semi – continuity in topological spaces”, Amer. Math.
Monthly, 70(1) 36 – 41, (1963).
[4] Kelley J. C., “Bitopological spaces”, Proc. London Math. Soc., 13(3) 71-89, (1963).
[5] Hardi N. A., “( ) open set in bitopological spaces”, Int. J. of Scientific and
Engineering research, 3(10), (2012).
[6] Erdal Ecici, “On contra πg-continuous functions”, Choas Solitons and fractals, 35,
71-81, (2008).
[7] Dontchev J. and Noiri T., “Contra semi – continuous functions”, Math. Pannon, 10(2), 159 –
168, (1999).
[8] Crossely S. G. and Hildebrand S. K., “Semi – closure”, Texas J. Sci., 22, 99 –112, (1971).
[9] Carnahan D. A., “Some properties related to compactness in topological spaces”, Ph.D. Thesis,
Univ. Arkanas, 1973.
[10] Alias Barakat Khalaf, Hardi Nasraddin Aziz and Hardi Ali Sharef,“( ) Continuous
and ( ) continuous Functions”, Journal of University of Zakho, Vol.1, No.1, 338-349 ,2013.