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Sg- Continuity in Topological Spaces.

Halgwrd M. Darwesh1 & Nawroz O.Hassan2

1 Mathematics Department, School of Science , Faculty of Science and Science Education, University of Sulaimani
2 Kurdistan Institution for Strategic students and scientific Research, Department of Information and Technology

The aim of the present paper, is to introduce and study a new class of functions which is
strictly placed between the class of  -continuous functions and the class of semi-continuous function, we call it the class of -continuous functions. The basic properties, characterizations and relationships with some other classes of continuity are
also obtained.

Key Words: Sg-open set, Semi-open set, g-closed set, Sg-continuous Function


[1] Abd-El-Monsef M. E., El-Deeb S. N. and Mahmoud R. A. , “β-open sets and β-continuous
mappings”, Bull. Fac. Assint, Vol. 12, 77-90, (1983).
[2] Darwesh H. M., “A new Type of Semi-open sets and Semi- Continuity in Topological
Spaces”, Zanko J. of Pure and Appl. Sci., Vol. 23, No.2, 82-92, (2011).
[3] Darwesh H. M. and Hessean N. O., “ Sp-open sets in topological spaces”, J. of Zankoy

Sulaimani for Pure and Appl. Sci., in press (2015).
[4] Dontchev J., “Survey on preopen sets”, ArXvi Math., Vol. 1, 1-18, (1998).
[5] Dontchev J., “Contra-continuous functions and strongly S-closed spaces”, Int. J. Math. and
Math. Sci.,
Vol. 19, No. 2, 303-310, (1996).
[6] Dontchev J. and Noiri T., “Contra-semi continuous functions”, Math. Pannon, Vol. 10, No. 2,
159-168, (1999).
[7] Guo T. Y., “A characterization of extermally disconnected spaces”, J. central china Normal
Univ. Nature. Sci., Vol. 12, No. 2, 169-170, (1981).

[8] Jafari S. and Noiri T., “On contra-precontinuous functions”, Bull. Malays. Math. Sci., Vol. 25,
No. 2, 115-128, (2002).
[9] Jafari S. and Noiri T., “Contra α-continuous functions between topological spaces”, Iran. Int. J.
Sci., Vol. 2, No. 2, 153-167, (2001).
[10] Jain R. C., “The role of regularly open sets in general topology”, Ph.D. Thesis, Meerut Univ.
Institute of advanced studies, Meerut-India, (1980).
[11] Joseph J. E. and Kwack M. H., “ On S-closed spaces”, Proc. Amer. Math. Soc.,
Vol. 80, No. 2, 341-348, (1980).
[12] Khalaf A. B. and Ahmed N. K., “ (-open sets and (-continuity in topological spaces”, THAI
J. of Math. Monthly, Vol. 70, No. 1, 319-335, (2013).
[13] Khalaf A. B. and Aameen Z. A., “ %-open sets and %-continuity in topological spaces”, J. of

Advanced Research in Pure Math. Vol. 2, No. 3, 87-101, (2010).
[14] Khalaf A. B. and Easif F. H., “ "+-continuous functions”, J. Dohuk Univ., special issue, 1-4,
[15] Khalaf A. B., Majeed A. H. and Jamil J. M., “ 2-open sets and 2-continuous Functions”, Int.J. of Advanced Math. Sci., Vol. 2, No. 1, 71-80, (2014).
[16] Levin N., “Generalized closed sets in topology”, Rend. Circ. Math. Paleremo Vol. 19, No. 2,
89-96, (1970).
[17] Levine N., “Semi-open sets and semi-continuity in topological spaces”, Amer. Math. Monthly,
Vol. 70, 36-41, (1963).
[18] Majid M., “ A note on extermally disconnected spaces”, Research Open J. of Information
Sci., Vol. 1, No. 1, 01-03, (2013).
[19] Mashhour A. S., Abd El-Monsef M. E. and El-Deeb S. N. “On precontinuous and weak
precontinuous functions”, Proc. Math. Phy. Soc. Egypt, Vol. 53, 47-53, (1982).
[20] Mashhour A. S., Hasanein I. A. and El-Deeb S. N., “A note on semi-continuity and
precontinuity”, Indian J. Pure Appl. Math. Vol. 13, No. 10, 1119-1123, (1982).
[21] Mashhour A. S., Hasanein I. A. and El-Deeb S. N., “ -continuous and -open mapping”,
Acta Math. Hung., Vol. 41, No. (3-4), 213-218, (1983).
[22] MOIZ-UD-DIN KHAN, “Weak forms of continuity, compactness and connectedness”, Ph.D.
Thesis, Bahauddin Zakariya Univ. Multan, Pakistan, (1997).
[23] Munshi B. M. and Bassan D. S., “Super continuous functions”, Indian J. Pure Appl. Math.,
Vol. 13, No. 2, 229-236, (1982).
[24] Njastad O., “On some classes of nearly open sets”, Pacific J. Math., Vol. 15, No. 3, 961-970,
[25] Noiri T. , “Super continuity and some strong forms of continuity”, Indian J. Pure Appl. Math.,
Vol. 15, No. 3, 241-250, (1984).
[26] Noiri T. and Popa V., “Weak forms of faint continuity”, Bull. Math. de la Soc. Sci. Math. de
la Roumanie, Vol. 34,No. 82, 263-270, (1990).
[27] Nour T. M., “Totally semi-continuous functions”, Indian J. Pure Appl. Math., Vol. 26, No. 7,
675-678, (1995).
[28] Park J. H., Lee B. Y., and Son M. J., “On -semi-open sets in topological spaces”, J. Indian
Acad. Math. Vol. 19, No. 1, 59-67, (1997).
[29] Reilly I. L. and Vamanmurthy, “On super-continuous functions”, Indian J. Pure Appl. Math.,
Vol. 14, 767-772, (1983).

[30] Shareef H. A., “ Sp -open sets, Sp-continuity and Sp-compactness in Topological spaces”,
M.Sc. Thesis, Univ. of Sulaimani, (2007).
[31] Simmons G. F., “Topology and Modern Analysis”, Tata McGraw Hill, (1963).
[32] Steen L. A. and Seebach J. A., “Counterexamples in Topology, Springer Verlag New York
Heidelberg Berlin, (1978).
[33] Stone M. H., “Algebraic characterizations of special Boolean rings”, Fund. Math., Vol. 29,
223-302, (1937).
[34] Velicko N. V. , “H-closed topological spaces”, Amer. Math. Soc. Transl., (1968).
Vol. 78, No. 2, 103-118.
[35] Willard S., “General Topology”, Addison-Wesley Publishing Company, (1970).
[36] Yunis R. H., “Properties of θ-semi-open sets”, Zanco J. of Pure and Appl. Sci., Vol. 19, No.
1, 116-122, (2007).