Hardi A. Shareef1, Hardi N. Aziz2 & Halgwrd M. Darwesh1

1 University of Sulaimani, Faculty of Science and Science Education, School of Science, Department of Mathematics

2 University of Sulaimani, Faculty of Science and Science Education, School of Science Education, Department of Mathematics,

**Abstract**

The aim of this work is to introduce a new generalization of a pre-connected space,

which is called -connected space and study relationship with other types of connected

spaces and gives some results on it. Further results concerning preservation of this

connectedness like properties under surjections are obtained.

which is called -connected space and study relationship with other types of connected

spaces and gives some results on it. Further results concerning preservation of this

connectedness like properties under surjections are obtained.

**Key Words:**Ps-open set; - separated sets; - connected spaces.

**References**

[1] Steen L. A. and Seebach J. A., “Counterexamples in Topology”, Hollt, Rinehart and Winston,

Inc., New York, 1970.

[2] Sharma J. N., and Chauhan J. P., “Topology (general and algebraic)”, Krishna Prakashsan

Media, Indai, 2011.

[3] Navalagi G. B., “Completely preirresolute functions, completely gp-irresolute functions”, Dept.

of Math. G.H. College, Karnataka, India, pp. 1-13, 2001.

[4] Navalagi G. B., “Pre-neighborhoods”, The Mathematics Education, Vol. 32, No. 4, pp. 201- 206, 1998.

[5] Mashhour A. S., and Abd-El-Monsef M. E. and El-Deeb S. N., “On pre-continuous and weak

pre-continuous mappings”, Proc. Math. Phys. Soc. Egypt, Vol. 53, pp. 47-53, 1982.

[6] Maheshwari S. N. and Prasad R., “Some new separation axioms”, Ann. Soc. Sci. Bruxelles, Ser.

I., Vol. 89, pp. 395-402, 1975.

[7] Jafari S., and Noiri T., “Properties of -connected spaces”, Acta Math. Hungar., Vol. 101 (3),

pp. 227-236, 2003.

[8] Dontchev J., Ganster M. and Noiri T.,“On p-closed spaces”, Internat. J. Math. and Math. Sci.,

Vol. 24, No. 3, pp. 203-212, 2000.

[9] Dontchev J., “Survey on preopen sets”, ArXiv: Math., Vol. 1, pp. 1-18, 1998.

[10] Dontchev J., “Contra-continuous functions and strongly s-closed spaces”, Inter. J. Math. and

Math. Sci., Vol. 19, No. 2, pp. 303-310, 1996.

[11] Crossley S. G., and Hildebrand S. K., “Semi-closure”, Texas J. Sci., Vol. 22, pp. 99-112, 1971.

[12] Cameron D. E., “Properties of S-closed spaces”, Proc. Amer. Math. Soc., Vol. 72, No. 3, pp.

581-586, 1978.

[13] Asaad B. A., “Utilization of some types of preopen sets in topological spaces”, M.Sc. Thesis,

University of Dohuk, Iraq, 2007.

[14] Abd-El-Monsef M. E., El-Deeb S. N. and Mahmoud R. A., “-open sets and -continuous mapping"s, Bull. Fac. Assint, Vol. 12, pp. 77-90, 1983