Regular Generalized <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math>-Closed Sets

Al-Omari, Ahmad; Noorani, Mohd Salmi Md

doi:https://doi.org/10.1155/2007/16292

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 016292 | https://doi.org/10.1155/2007/16292

Regular Generalized ω-Closed Sets

Ahmad Al-Omari¹and Mohd Salmi Md Noorani¹

Academic Editor: Lokenath Debnath

Received12 Sept 2006

Revised01 Dec 2006

Accepted16 Jan 2007

Published26 Apr 2007

Abstract

In 1982 and 1970, Hdeib and Levine introduced the notions of ω-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalized ω-closed, regular generalized ω-continuous, a-ω-continuous, and regular generalized ω-irresolute maps and to study its fundamental properties.

References

S. Willard, General Topology, Addison-Wesley, Reading, Mass, USA, 1970.
View at: Zentralblatt MATH | MathSciNet
H. Z. Hdeib, “ $ω$ -closed mappings,” Revista Colombiana de Matemáticas, vol. 16, no. 1-2, pp. 65–78, 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
K. Y. Al-Zoubi, “On generalized $ω$ -closed sets,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 13, pp. 2011–2021, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
H. Z. Hdeib, “ $ω$ -continuous functions,” Dirasat Journal, vol. 16, no. 2, pp. 136–153, 1989.
View at: Google Scholar
N. Levine, “Generalized closed sets in topology,” Rendiconti del Circolo Matematico di Palermo. Serie II, vol. 19, pp. 89–96, 1970.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
S. P. Arya and T. M. Nour, “Characterizations of $s$ -normal spaces,” Indian Journal of Pure and Applied Mathematics, vol. 21, no. 8, pp. 717–719, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
H. Maki, R. Devi, and K. Balachandran, “Associated topologies of generalized $α$ -closed sets and $α$ -generalized closed sets,” Memoirs of the Faculty of Science Kochi University. Series A. Mathematics, vol. 15, pp. 51–63, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
J. Dontchev and H. Maki, “On $θ$ -generalized closed sets,” International Journal of Mathematics and Mathematical Sciences, vol. 22, no. 2, pp. 239–249, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
J. Dontchev, “On generalizing semi-preopen sets,” Memoirs of the Faculty of Science Kochi University. Series A. Mathematics, vol. 16, pp. 35–48, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
J. Dontchev and M. Ganster, “On $δ$ -generalized closed sets and $T_{3 / 4}$ -spaces,” Memoirs of the Faculty of Science Kochi University. Series A. Mathematics, vol. 17, pp. 15–31, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
T. A. Al-Hawary, “ $ω$ -generalized closed sets,” International Journal of Applied Mathematics, vol. 16, no. 3, pp. 341–353, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
N. Palaniappan and K. C. Rao, “Regular generalized closed sets,” Kyungpook Mathematical Journal, vol. 33, no. 2, pp. 211–219, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
I. A. Rani and K. Balachandran, “On regular generalised continuous maps in topological spaces,” Kyungpook Mathematical Journal, vol. 37, no. 2, pp. 305–314, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
R. Engelking, General Topology, vol. 6 of Sigma Series in Pure Mathematics, Heldermann, Berlin, Germany, 2nd edition, 1989.
View at: Zentralblatt MATH | MathSciNet
W. Dunham, “ $T_{1 / 2}$ -spaces,” Kyungpook Mathematical Journal, vol. 17, no. 2, pp. 161–169, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
C. W. Baker, “On preserving $g$ -closed sets,” Kyungpook Mathematical Journal, vol. 36, no. 1, pp. 195–199, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
F. H. Khedr and T. Noiri, “On $θ$ -irresolute functions,” Indian Journal of Mathematics, vol. 28, no. 3, pp. 211–217, 1986.
View at: Google Scholar | Zentralblatt MATH | MathSciNet

Copyright

Copyright © 2007 Ahmad Al-Omari and Mohd Salmi Md Noorani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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