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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2196743, 6 pages
http://dx.doi.org/10.1155/2016/2196743
Research Article

A New Approach to Hausdorff Space Theory via the Soft Sets

Department of Mathematics, Faculty of Arts and Science, Amasya University, 05100 Amasya, Turkey

Received 1 April 2016; Accepted 8 August 2016

Academic Editor: Anna M. Gil-Lafuente

Copyright © 2016 Güzide Şenel. 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. D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. D. A. Molodtsov, “The description of a dependence with the help of soft sets,” Journal of Computer and Systems Sciences International, vol. 40, no. 6, pp. 977–984, 2001. View at Google Scholar
  3. D. Molodtsov, The Theory of Soft Sets, URSS Publishers, Moscow, Russia, 2004 (Russian).
  4. D. A. Molodtsov, V. Y. Leonov, and D. V. Kovkov, “Soft sets technique and its application,” Nechetkie Sistemy i Myagkie Vychisleniya, vol. 1, no. 1, pp. 8–39, 2006. View at Google Scholar
  5. H. Aktaş and N. Çağman, “Soft sets and soft groups,” Information Sciences, vol. 177, no. 13, pp. 2726–2735, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir, “On some new operations in soft set theory,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1547–1553, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Aygünoğlu and H. Aygün, “Some notes on soft topological spaces,” Neural Computing and Applications, vol. 21, supplement 1, pp. 113–119, 2011. View at Publisher · View at Google Scholar
  8. N. Çağman and S. Enginoğlu, “Soft matrix theory and its decision making,” Computers & Mathematics with Applications, vol. 59, no. 10, pp. 3308–3314, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. N. Çağman and S. Enginoğlu, “Soft set theory and uni-int decision making,” European Journal of Operational Research, vol. 207, pp. 848–855, 2010. View at Google Scholar
  10. N. Çağman, “Contributions to the theory of soft sets,” Journal of New Result in Science, vol. 4, pp. 33–41, 2014. View at Google Scholar
  11. D. N. Georgiou and A. C. Megaritis, “Soft set theory and topology,” Applied General Topology, vol. 15, no. 1, pp. 93–109, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. O. Kazanci, S. Yilmaz, and S. Yamak, “Soft sets and soft BCH-algebras,” Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, pp. 205–217, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  13. P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555–562, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1077–1083, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. K. Maji, R. Biswas, and A. R. Roy, “Fuzzy soft sets,” Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589–602, 2001. View at Google Scholar · View at MathSciNet
  16. Y. Zou and Z. Xiao, “Data analysis approaches of soft sets under incomplete information,” Knowledge-Based Systems, vol. 21, no. 8, pp. 941–945, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. K. V. Babitha and J. J. Sunil, “Soft set relations and functions,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1840–1849, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. E. F. Lashin, A. M. Kozae, A. A. Abo Khadra, and T. Medhat, “Rough set theory for topological spaces,” International Journal of Approximate Reasoning, vol. 40, no. 1-2, pp. 35–43, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. W. K. Min, “A note on soft topological spaces,” Computers & Mathematics with Applications, vol. 62, no. 9, pp. 3524–3528, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. E. Peyghan, B. Samadi, and A. Tayebi, “About soft topological spaces,” Journal of New Results in Science, vol. 2, pp. 60–75, 2013. View at Google Scholar
  21. G. Şenel, Soft metric spaces, gaziosmanpas [Ph.D. thesis], University Graduate School of Natural and Applied Sciences Department of Mathematics, 2013.
  22. M. Shabir and M. Naz, “On soft topological spaces,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1786–1799, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. I. Zorlutuna, M. Akdağ, W. K. Min, and S. Atmaca, “Remarks on soft topological spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 3, no. 2, pp. 171–185, 2012. View at Google Scholar · View at MathSciNet
  24. J. C. Kelly, “Bitopological spaces,” Proceedings of the London Mathematical Society, vol. 13, no. 3, pp. 71–89, 1963. View at Google Scholar · View at MathSciNet
  25. L. Motchane, “Sur La Notion Diespace Bitopologique et Sur Les Espaces de Baire,” Comptes Rendus de l'Académie des Sciences, vol. 224, pp. 3121–3124, 1957. View at Google Scholar
  26. A. A. Ivanov, “Problems of the theory of bitoplogical spaces,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), vol. 167, no. 6, pp. 5–62, 1988 (Russian), English Translation: Journal of Soviet Mathematics, vol. 52, no. 1, pp. 2759–2790, 1990. View at Google Scholar
  27. G. C. L. Brümmer, “Two procedures in bitopology,” in Categorical Topology: Proceedings of the International Conference, Berlin, August 27th to September 2nd, 1978, vol. 719 of Lecture Notes in Mathematics, pp. 35–43, Springer, Berlin, Germany, 1979. View at Publisher · View at Google Scholar
  28. M. C. Datta, “Projective bitopological spaces,” Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics, vol. 13, pp. 327–334, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  29. M. C. Datta, “Projective bitopological spaces, II,” Journal of the Australian Mathematical Society, vol. 14, no. 1, pp. 119–128, 1972. View at Publisher · View at Google Scholar
  30. B. P. Dvalishvili, Bitoplogical Spaces; Theory, Relations with Generalized Algebraic Structures, and Applications, vol. 199 of North-Holland Mathematical Studies, Elsevier Science, 2005.
  31. C. W. Patty, “Bitopological spaces,” Duke Mathematical Journal, vol. 34, pp. 387–391, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  32. D. Adnadjević, “Ordered spaces and bitopology,” Glasnik Matematički Serija III, vol. 10, no. 30, pp. 337–340, 1975. View at Google Scholar · View at MathSciNet
  33. B. Banaschewski and G. C. Brummer, “Stably continuous frames,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 1, pp. 7–19, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  34. H. A. Priestley, “Ordered topological spaces and the representation of distributive lattices,” Proceedings London Mathematical Society, vol. 24, no. 3, pp. 507–530, 1972. View at Google Scholar
  35. O. Ravi and M. L. Thivagar, “A bitopological (1, 2) semi-generalised continuous maps,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 29, no. 1, pp. 79–88, 2006. View at Google Scholar
  36. R. E. Smithson, “Multifunctions and bitopological spaces,” Journal of Natural Sciences and Mathematics, vol. 11, pp. 191–198, 1971. View at Google Scholar · View at MathSciNet
  37. S. Hussain and B. Ahmad, “Some properties of soft topological spaces,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4058–4067, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. N. Çağman, S. Karatas, and S. Enginoğlu, “Soft topology,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 351–358, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. G. Şenel and N. Çağman, “Soft topological subspaces,” Annals of Fuzzy Mathematics and Informatics, vol. 10, no. 4, pp. 525–535, 2015. View at Google Scholar · View at MathSciNet