Bc-Open Sets in Topological Spaces

ABSTRACT

In this paper, we introduce a new class of*b*-open sets called *Bc*-open, this class of sets lies strictly between the classes of *θ*-semi open and *b*-open sets. We also study its fundamental properties and compare it with some other types of sets and we investigate further topological properties of sets and we introduce and investigate new class of space named *Bc*-compact.

In this paper, we introduce a new class of

Cite this paper

H. Ibrahim, "Bc-Open Sets in Topological Spaces,"*Advances in Pure Mathematics*, Vol. 3 No. 1, 2013, pp. 34-40. doi: 10.4236/apm.2013.31007.

H. Ibrahim, "Bc-Open Sets in Topological Spaces,"

References

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[10] G. Di Maio and T. Noiri, “On s-Closed Spaces,” Indian Journal of Pure and Applied Mathematics, Vol. 18, No. 3, 1987, pp. 226-233.

[11] D. Andrijevic, “On b-Open Sets,” Matemati?ki Vesnik, Vol. 48, No. 3, 1996, pp. 59-64.

[12] J. Dontchev and T. Noiri, “Contra-Semicontinuous Functions,” Mathematica Pannonica, Vol. 10, No. 2, 1999, pp. 159-168.

[13] R. H. Yunis, “Properties of θ-Semi-Open Sets,” Zanco Journal of Pure and Applied Sciences, Vol. 19, No. 1, 2007, pp. 116-122.

[14] M. H. Stone, “Algebraic Characterizations of Special Boolean Rings,” Fundamenta Mathematicae, Vol. 29, No. 1, 1937, pp. 223-302.

[15] J. Dontchev, “Survey on Preopen Sets,” The Proceedings of the Yatsushiro Topological Conference, 22-23 August 1998, pp. 1-18.

[1] M. H. Stone, “Applications of the Theory of Boolean Rings to Topology,” Transactions of the American Mathematical Society, Vol. 41, No. 3, 1937, pp. 375-481. doi:10.1090/S0002-9947-1937-1501905-7

[2] N. Levine, “Semi-Open Sets and Semi-Continuity in Topological Spaces,” American Mathematical Monthly, Vol. 70, No. 1, 1963, pp. 36-41. doi:10.2307/2312781

[3] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, “On Precontinuous and Week Precontinuous Mappings,” Proceedings of Mathematical and Physical Society of Egypt, Vol. 53, 1982, pp. 47-53.

[4] O. Njastad, “On Some Classes of Nearly Open Sets,” Pacific Journal of Mathematics, Vol. 15, No. 3, 1965, pp. 961-970. doi:10.2140/pjm.1965.15.961

[5] S. N. El-Deeb, I. A. Hasanein, A. S. Mashhour and T. Noiri, “On p-Regular Spaces,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, Vol. 27, No. 4, 1983, pp. 311-315.

[6] S. G. Crossley and S. K. Hildebrand, “Semi-Closure,” Texas Journal of Science, Vol. 22, No. 2-3, 1971, pp. 99-112.

[7] J. E. Joseph and M. H. Kwack, “On S-Closed Spaces,” Bulletin of the American Mathematical Society, Vol. 80, No. 2, 1980, pp. 341-348.

[8] N. K. Ahmed, “On Some Types of Separation Axioms,” M.Bc. Thesis, Salahaddin University, Arbil, 1990.

[9] N. V. Velicko, “H-Closed Topological Spaces,” American Mathematical Society, Vol. 78, No. 2, 1968, pp. 103-118.

[10] G. Di Maio and T. Noiri, “On s-Closed Spaces,” Indian Journal of Pure and Applied Mathematics, Vol. 18, No. 3, 1987, pp. 226-233.

[11] D. Andrijevic, “On b-Open Sets,” Matemati?ki Vesnik, Vol. 48, No. 3, 1996, pp. 59-64.

[12] J. Dontchev and T. Noiri, “Contra-Semicontinuous Functions,” Mathematica Pannonica, Vol. 10, No. 2, 1999, pp. 159-168.

[13] R. H. Yunis, “Properties of θ-Semi-Open Sets,” Zanco Journal of Pure and Applied Sciences, Vol. 19, No. 1, 2007, pp. 116-122.

[14] M. H. Stone, “Algebraic Characterizations of Special Boolean Rings,” Fundamenta Mathematicae, Vol. 29, No. 1, 1937, pp. 223-302.

[15] J. Dontchev, “Survey on Preopen Sets,” The Proceedings of the Yatsushiro Topological Conference, 22-23 August 1998, pp. 1-18.