On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>I</mml:mi></mml:math>-Open Sets and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>I</mml:mi></mml:math>-Continuous Functions

Akdağ, Metin

doi:https://doi.org/10.1155/2007/75721

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 075721 | https://doi.org/10.1155/2007/75721

On b-I-Open Sets and b-I-Continuous Functions

Metin Akdağ¹

Academic Editor: Sehie Park

Received02 Mar 2007

Revised23 May 2007

Accepted30 Aug 2007

Published30 Oct 2007

Abstract

We studied some more properties of b-I-open sets and obtained several characterizations of b-I-continuous functions which are introduced by Caksu Guler and Aslim (2005). We also investigated their relationship with other types of functions.

References

D. Janković and T. R. Hamlett, “New topologies from old via ideals,” The American Mathematical Monthly, vol. 97, no. 4, pp. 295–310, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
D. Janković and T. R. Hamlett, “Compatible extensions of ideals,” Unione Matematica Italiana. Bollettino. B. Serie VII, vol. 6, no. 3, pp. 453–465, 1992.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
M. E. Abd El-Monsef, E. F. Lashien, and A. A. Nasef, “On $I$ -open sets and $I$ -continuous functions,” Kyungpook Mathematical Journal, vol. 32, no. 1, pp. 21–30, 1992.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
J. Dontchev, “On pre- $I$ open sets and a decomposition of $I$ continuity,” Banyan Mathematical Journal, vol. 2, 1996.
View at: Google Scholar
E. Hatir and T. Noiri, “On decompositions of continuity via idealization,” Acta Mathematica Hungarica, vol. 96, no. 4, pp. 341–349, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. Hatir and T. Noiri, “On semi- $I$ -open sets and semi- $I$ -continuous functions,” Acta Mathematica Hungarica, vol. 107, no. 4, pp. 345–353, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
A. Caksu Guler and G. Aslim, “ $b$ - $I$ -open sets and decomposition of continuity via idealization,” Proceedings of Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan, vol. 22, pp. 27–32, 2005.
View at: Google Scholar | MathSciNet
R. Vaidyanathaswamy, “The localisation theory in set-topology,” Proceedings of the Indian Academy of Sciences, vol. 20, pp. 51–61, 1944.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
E. Hayashi, “Topologies defined by local properties,” Mathematische Annalen, vol. 156, pp. 205–215, 1964.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
P. Samuels, “A topology formed from a given topology and ideal,” Journal of the London Mathematical Society, vol. 10, no. 4, pp. 409–416, 1975.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
O. Njȧstad, “On some classes of nearly open sets,” Pacific Journal of Mathematics, vol. 15, pp. 961–970, 1965.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
N. Levine, “Semi-open sets and semi-continuity in topological spaces,” The American Mathematical Monthly, vol. 70, no. 1, pp. 36–41, 1963.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deep, “On precontinuous and weak precontinuous mappings,” Proceedings of the Mathematical and Physical Society of Egypt, no. 53, pp. 47–53, 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
A. S. Mashhour, I. A. Hasanein, and S. N. El-Deeb, “ $α$ -continuous and $α$ -open mappings,” Acta Mathematica Hungarica, vol. 41, no. 3-4, pp. 213–218, 1983.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
A. A. El-Atik, “A study of some types of mappings on topological spaces,” M. Sci. thesis, Tanta University, Tanta, Egypt, 1997.
View at: Google Scholar
D. Andrijević, “On $b$ -open sets,” Matematichki Vesnik, vol. 48, no. 1-2, pp. 59–64, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
T. Noiri, “Hyperconnectedness and pre-open sets,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 29, no. 4, pp. 329–334, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
J. Dontchev, “Idealization of Ganster-Reilly decomposition theorems,” 1999, http://arxiv.org/abs/Math.GN/9901017.
View at: Google Scholar
M. Mršević, “On pairwise $R_{0}$ and pairwise $R_{1}$ bitopological spaces,” Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série, vol. 30(78), no. 2, pp. 141–148, 1986.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
S. Jafari and T. Noiri, “Contra-super-continuous functions,” Annales Universitatis Scientiarum Budapestinensis, vol. 42, pp. 27–34, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
R. L. Newcomb, “Topologies which are compact modulo an ideal,” Ph.D. dissertation, University of California, Santa Barbara, Calif, USA, 1967.
View at: Google Scholar
R. Staum, “The algebra of bounded continuous functions into a nonarchimedean field,” Pacific Journal of Mathematics, vol. 50, pp. 169–185, 1974.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
A. A. Nasef and A. S. Farrag, “Completely $b$ -irresolute functions,” Proceedings of the Mathematical and Physical Society of Egypt, no. 74, pp. 73–86, 1999.
View at: Google Scholar | MathSciNet

Copyright

Copyright © 2007 Metin Akdağ. 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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