Table of Contents
Chinese Journal of Mathematics
Volume 2013, Article ID 412391, 6 pages
http://dx.doi.org/10.1155/2013/412391
Research Article

On Faintly Continuous Functions via Generalized Topology

Department of Mathematics, Women’s Christian College, 6 Greek Church Row, Kolkata 700 026, India

Received 13 July 2013; Accepted 9 September 2013

Academic Editors: Y. Ouyang, G. Wang, and W. Zhu

Copyright © 2013 Bishwambhar Roy. 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.

Linked References

  1. Á. Császár, “Generalized topology, generalized continuity,” Acta Mathematica Hungarica, vol. 96, no. 4, pp. 351–357, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Á. Császár, “Generalized open sets in generalized topologies,” Acta Mathematica Hungarica, vol. 106, no. 1-2, pp. 53–66, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Á. Császár, “δ- and θ-modifications of generalized topologies,” Acta Mathematica Hungarica, vol. 120, no. 3, pp. 275–279, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Á. Császár, “Separation axioms for generalized topologies,” Acta Mathematica Hungarica, vol. 104, no. 1-2, pp. 63–69, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Á. Császár, “γ-connected sets,” Acta Mathematica Hungarica, vol. 101, no. 4, pp. 273–279, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. N. V. Veličko, “H-closed topological spaces,” Matematicheskii Sbornik, vol. 70, no. 112, pp. 98–112, 1966. View at Google Scholar · View at MathSciNet
  7. N. Levine, “Semi-open sets and semi-continuity in topological spaces,” The American Mathematical Monthly, vol. 70, pp. 36–41, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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, vol. 53, pp. 47–53, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. O. Njȧstad, “On some classes of nearly open sets,” Pacific Journal of Mathematics, vol. 15, pp. 961–970, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, “β-open sets and β-continuous mapping,” Bulletin of the Faculty of Science. Assiut University A, vol. 12, no. 1, pp. 77–90, 1983. View at Google Scholar · View at MathSciNet
  11. D. Andrijević, “Semi-preopen sets,” Matematički Vesnik, vol. 38, pp. 24–32, 1986. View at Google Scholar
  12. S. Raychaudhuri and M. N. Mukherjee, “On δ-almost continuity and δ-preopen sets,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 21, no. 4, pp. 357–366, 1993. View at Google Scholar · View at MathSciNet
  13. J. H. Park, D. S. Song, and R. Saadati, “On generalized δ-semiclosed sets in topological spaces,” Chaos, Solitons and Fractals, vol. 33, no. 4, pp. 1329–1338, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. E. Ekici, “On e-open sets DP*-sets DPE*-sets and decompositions of continuity,” The Arabian Journal for Science and Engineering A, vol. 33, no. 2, pp. 269–282, 2008. View at Google Scholar · View at MathSciNet
  15. G. Di Maio and T. Noiri, “On s-closed spaces,” Indian Journal of Pure and Applied Mathematics, vol. 18, no. 3, pp. 226–233, 1987. View at Google Scholar · View at MathSciNet
  16. M. C. Pal and P. Bhattacharyya, “Feeble and strong forms of preirresolute functions,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 19, no. 2, pp. 63–75, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Dontchev and T. Noiri, “Quasi-normal spaces and πg-closed sets,” Acta Mathematica Hungarica, vol. 89, no. 3, pp. 211–219, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  18. H. Z. Hdeib, “ω-closed mappings,” Revista Colombiana de Matemáticas, vol. 16, no. 1-2, pp. 65–78, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. B. Roy, “Unification of almost strongly μθ-continuous functions,” accepted in Le Mathematiche.
  20. P. E. Long and L. L. Herrington, “The Tθ-topology and faintly continuous functions,” Kyungpook Mathematical Journal, vol. 22, no. 1, pp. 7–14, 1982. View at Google Scholar · View at MathSciNet
  21. T. Noiri and V. Popa, “Weak forms of faint continuity,” Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, vol. 34, no. 3, pp. 263–270, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. Jafari and T. Noiri, “On faintly α-continuous functions,” Indian Journal of Mathematics, vol. 42, no. 2, pp. 203–210, 2000. View at Google Scholar · View at MathSciNet
  23. A. A. Nasef, “Another weak form of faint continuity,” Chaos, Solitons and Fractals, vol. 12, no. 12, pp. 2219–2225, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. E. Ekici, “On almost continuity,” Kyungpook Mathematical Journal, vol. 46, no. 1, pp. 119–130, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. E. Ekici, “On δ-semiopen sets and a generalization of functions,” Boletim da Sociedade Paranaense de Matemática, vol. 23, no. 1-2, pp. 73–84, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  26. M. C. Caldas, “On the faintly e-continuous functions,” Sarajevo Journal of Mathematics, vol. 8, no. 1, pp. 159–170, 2012. View at Google Scholar · View at MathSciNet
  27. A. A. El-Atik, “On some types of faint continuity,” Thai Journal of Mathematics, vol. 9, no. 1, pp. 83–93, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. N. Rajesh, “On faintly πg-continuous functions,” Boletim da Sociedade Paranaense de Matemática, vol. 30, no. 1, pp. 9–19, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  29. E. Ekici, S. Jafari, and S. P. Moshokoa, “On a weaker form of ω-continuity,” Annals of the University of Craiova. Mathematics and Computer Science Series, vol. 37, no. 2, pp. 38–46, 2010. View at Google Scholar · View at MathSciNet
  30. T. Noiri and V. Popa, “Faintly m-continuous functions,” Chaos, Solitons and Fractals, vol. 19, no. 5, pp. 1147–1159, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  31. M. K. Singal and S. Prabha Arya, “On almost-regular spaces,” Glasnik Matematički, vol. 4, no. 24, pp. 89–99, 1969. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. T. Noiri, “Slightly β-continuous functions,” International Journal of Mathematics and Mathematical Sciences, vol. 28, no. 8, pp. 469–478, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  33. R. L. Ellis, “A non-Archimedean analogue of the Tietze-Urysohn extension theorem,” Indagationes Mathematicae, vol. 29, pp. 332–333, 1967. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. M. S. Sarsak, “Weak separation axioms in generalized topological spaces,” Acta Mathematica Hungarica, vol. 131, no. 1-2, pp. 110–121, 2011. View at Publisher · View at Google Scholar
  35. S. Sinharoy and S. Bandyopadhyay, “On θ-completely regular and locally θ-H-closed spaces,” Bulletin of the Calcutta Mathematical Society, vol. 87, no. 1, pp. 19–26, 1995. View at Google Scholar · View at MathSciNet
  36. M. C. Caldas, S. Jafari, and T. Noiri, “Some separation axioms via modified θ-open sets,” Bulletin of the Iranian Mathematical Society, vol. 29, no. 2, pp. 1–12, 2003. View at Google Scholar · View at MathSciNet
  37. B. Roy, “On a type of generalized open sets,” Applied General Topology, vol. 12, no. 2, pp. 163–173, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. R.-X. Shen, “A note on generalized connectedness,” Acta Mathematica Hungarica, vol. 122, no. 3, pp. 231–235, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. B. Roy and S. Jafari, “On covering properties via generalized open sets,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Mathematica, vol. 55, pp. 57–65, 2012. View at Google Scholar · View at MathSciNet
  40. S. Jafari, “Some properties of quasi θ-continuous functions,” Far East Journal of Mathematical Sciences, vol. 6, no. 5, pp. 689–696, 1998. View at Google Scholar · View at MathSciNet