On almost and weakly i p -continuous functions in topological space.

Laila S. Abdullah and Diyar M. Mohammed

Dept. of Mathematics, / Faculty of Science and Science Education/ School of science, University of Sulaimani, Kurdistan Region
Dept. of Mathematics, Faculty of Physical and Basic Education/ School of Basic Education, University of Sulaimani, Kurdistan


In this paper, we introduce two new classes of continuous functions in topological spaces
called almost Ip-continuous and weakly Ip-continuous functions. We obtain several
characterizations of them and some of their properties. Also, we investigate their
relationships with some other types of functions.

Key Words:
set, Ip-open set, Ip-
continuous function,
Almost Ip-continuous
function, Weakly Ip-
continuous function.


[1] Abdul-jabber A. M., " s-continuity, openness and closed graphs in topological Space", M. Sc. Thesis, College of Science, Salahaddin Univ.(2000). 

[2] Abdullah L. S. and Mohammed D. M., "Ip-open sets, Ip-continuity, Ip-connectedness and Ip-separation axioms in topological spaces", M. Sc. Thesis, faculty of sc. and sc. edu., Sulaimani Univ., Faculty of physical and basic edu., univ. of Sulaimani.(2011). 

[3] Dontchev J. and Noiri T., “Contra-semi continuous Functions*”, arXiv: math. Vol.1, No. 12, pp. 1-12. (1998). 

[4] Dontchev J., "Survey on preopen sets", ArXiv:Math.Vol.1, pp. 1-18. (1998). 

[5] Fomin S., "Extensions of topological spaces", Ann. Of Math., 44(3), pp. 471- 480. (1943). 

[6] Levine N., " a decomposition of continuity in topological space" , Amer. Math. Monthly, pp. 36-41. (1961). 

[7] Maio G. D. and Nori T., "On s‐Closed spaces", Indian J. pure appl. Math., Vol. 18, No.3, pp. 226‐ 233. (1986). 

[8] Mashhour A. S., Abd El-Monsef M. E. and El-Deeb S. N., "On precontinuous and weak precontinuous functions, Proc. Math. Phys. Soc. Egypt 53, pp. 47-53. (1982). 

[9] Nasef A. A. and Noiri T., "Some weak forms of almost continuity", Acta Math. Hungar., 74(3), pp. 211- 219. (1997). 

[10] Njastad O., "on some classes of nearly open sets", Pacific J. Math.,15(3), pp. 961-970. (1965). 

[11] Reilly I. L. and Vamanmurthy M. K., "On -continuity in topological spaces", Acta Math. Hungar., 45(1-2),pp. 27-32. (1985) . 

[12] Velicko N. V., "H-closed topological space", Amer. Math. Soc. Transl., 78 (2), 103-1. (1968).