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Year 2014, Volume: 27 Issue: 4, 1077 - 1083, 03.06.2014

Abstract

References

  • M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory. Computer and Mathematics with Applications, 57 (2009) 1547-1553.
  • D. Molodtsov, Soft set theory-First results. Comput. Math. Appl. 37(4/5) (1999) 19-31.
  • P. K. Maji, R. Biswas and A. R. Roy, Soft set theory. Computer and Math. with Appl. (2003), 555- 562.
  • M. Shabir and M. Naz, On soft topological spaces. Comput. Math. Appl. 61 (2011) 1786-1799.
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces. Applied Mathematics & Information Sciences. 7(1) (2013) 287-294.
  • A. Aygunoglu and H.Aygun, Some notes on soft topological spaces. Neural Comput and Applic. Neural Comput. and Applic, 21(1) (2012) 113-119.
  • I. Arockiarani and A. A. Lancy, Generalized soft gβ- closed sets and soft gsβ-closed sets in soft topological spaces. International Journal Of Mathematical Archive, 4(2), (2013) 1-7.
  • I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3(2) (2012) 171-185.
  • S. Hussain and B. Ahmedi, Some properties of soft topological spaces. Neural Comput and Appl., 62 (2011) 4058-4067.
  • A. S Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuouıs mappings. Proc. Math. Phys. Soc. Egypt 53 (1982) 47- 53.
  • A. S Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semi-continuity and precontinuity. Indian J. Pure Apll. Math.13(10) (1982) 1119-1123.
  • T. Noiri, A. S Mashhour and S. N. El-Deeb, On p- regular spaces. Bull. Math. Soc. Sci. Math. R. S. Roumaine 27(75) (1983) 437-441.
  • Y. Gnanambal, On Generalized Preregular Closed Sets in topological Spaces. Indian J. Pure. Appl. Math., 28(3) (1997) 351-360.
  • J. Dontchev, I. Arokiarani.and K. Balachandran, Some characterizatoins of gp-irresolute and gp- continuous maps between topological spaces. Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 20 (1999).93-104. [15] E. Ekici, Almost contra-precontinuous functions. Bull Malays Math. Sci. Soc. 27(1) (2004) 53-65.
  • J. Dontchev and H. Maki, On behaviror of gp- closed sets and their generalizations. Mem. Fac. Sci. Kochi Univ. Math., 19 (1998) 57-72.
  • V.M.K.R.S. Kumar, Semi-pre-generalized closed sets. Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 20 (1999) 33-46.
  • S. Jafari and T. Noiri, On contra-precontinuous functions. Bull Malaysian Math. Sci. Soc. 25(2) (2002) 115-28.
  • T. Noiri, H. Maki and J. Umehara, Generalized preclosed functions. Men Fac. Sci. Kochi Univ. Ser. A, Math. 19 (1998) 13-20.
  • M. Akdag and A. Ozkan, Soft ߙ-open sets and soft ߙ-continuous functions. Abstract and Analysis Applied.(2014) 7 pages.
  • N. Cagman, S. Karatas and S. Enginoglu, Soft topology. Comput. Math. Appl. 62 (2011) 351-358
  • W. K. Min, A note on soft topological space. Computers And Mathematics With Applications, 62 (2011) 3524-3528.
  • B. Pazar, Varol and H. Aygun, On Soft Hausdorff Spaces. Ann. of Fuzzy Math. Inform, 5(1) (2013) 15-24. [24] L. Arokia and Arockiarani, On soft ߚ-separation axsioms. International Journal Of Mathematical Archive, Vol. 1 Issue 5, October-2013.

On Soft Preopen Sets and Soft Pre Separation Axioms

Year 2014, Volume: 27 Issue: 4, 1077 - 1083, 03.06.2014

Abstract

Arockiarani and Lancy [7], defined soft pre-open (closed) sets on soft topology. In this paper, we are continue investigating the properties of soft pre-open (closed) sets and define soft preclosure and soft preinterior in soft topological spaces. We are also introduce and research basic properties of the concepts of soft pre-regular spaces, soft P₃-spaces, soft pre-normal spaces and soft P₄-spaces in soft topological spaces, which are basic for further research on soft topology and will fortify the footing of the theory of soft topological space. 

References

  • M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory. Computer and Mathematics with Applications, 57 (2009) 1547-1553.
  • D. Molodtsov, Soft set theory-First results. Comput. Math. Appl. 37(4/5) (1999) 19-31.
  • P. K. Maji, R. Biswas and A. R. Roy, Soft set theory. Computer and Math. with Appl. (2003), 555- 562.
  • M. Shabir and M. Naz, On soft topological spaces. Comput. Math. Appl. 61 (2011) 1786-1799.
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces. Applied Mathematics & Information Sciences. 7(1) (2013) 287-294.
  • A. Aygunoglu and H.Aygun, Some notes on soft topological spaces. Neural Comput and Applic. Neural Comput. and Applic, 21(1) (2012) 113-119.
  • I. Arockiarani and A. A. Lancy, Generalized soft gβ- closed sets and soft gsβ-closed sets in soft topological spaces. International Journal Of Mathematical Archive, 4(2), (2013) 1-7.
  • I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3(2) (2012) 171-185.
  • S. Hussain and B. Ahmedi, Some properties of soft topological spaces. Neural Comput and Appl., 62 (2011) 4058-4067.
  • A. S Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuouıs mappings. Proc. Math. Phys. Soc. Egypt 53 (1982) 47- 53.
  • A. S Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semi-continuity and precontinuity. Indian J. Pure Apll. Math.13(10) (1982) 1119-1123.
  • T. Noiri, A. S Mashhour and S. N. El-Deeb, On p- regular spaces. Bull. Math. Soc. Sci. Math. R. S. Roumaine 27(75) (1983) 437-441.
  • Y. Gnanambal, On Generalized Preregular Closed Sets in topological Spaces. Indian J. Pure. Appl. Math., 28(3) (1997) 351-360.
  • J. Dontchev, I. Arokiarani.and K. Balachandran, Some characterizatoins of gp-irresolute and gp- continuous maps between topological spaces. Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 20 (1999).93-104. [15] E. Ekici, Almost contra-precontinuous functions. Bull Malays Math. Sci. Soc. 27(1) (2004) 53-65.
  • J. Dontchev and H. Maki, On behaviror of gp- closed sets and their generalizations. Mem. Fac. Sci. Kochi Univ. Math., 19 (1998) 57-72.
  • V.M.K.R.S. Kumar, Semi-pre-generalized closed sets. Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 20 (1999) 33-46.
  • S. Jafari and T. Noiri, On contra-precontinuous functions. Bull Malaysian Math. Sci. Soc. 25(2) (2002) 115-28.
  • T. Noiri, H. Maki and J. Umehara, Generalized preclosed functions. Men Fac. Sci. Kochi Univ. Ser. A, Math. 19 (1998) 13-20.
  • M. Akdag and A. Ozkan, Soft ߙ-open sets and soft ߙ-continuous functions. Abstract and Analysis Applied.(2014) 7 pages.
  • N. Cagman, S. Karatas and S. Enginoglu, Soft topology. Comput. Math. Appl. 62 (2011) 351-358
  • W. K. Min, A note on soft topological space. Computers And Mathematics With Applications, 62 (2011) 3524-3528.
  • B. Pazar, Varol and H. Aygun, On Soft Hausdorff Spaces. Ann. of Fuzzy Math. Inform, 5(1) (2013) 15-24. [24] L. Arokia and Arockiarani, On soft ߚ-separation axsioms. International Journal Of Mathematical Archive, Vol. 1 Issue 5, October-2013.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Metin Akdağ

Alkan Özkan

Publication Date June 3, 2014
Published in Issue Year 2014 Volume: 27 Issue: 4

Cite

APA Akdağ, M., & Özkan, A. (2014). On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science, 27(4), 1077-1083.
AMA Akdağ M, Özkan A. On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science. November 2014;27(4):1077-1083.
Chicago Akdağ, Metin, and Alkan Özkan. “On Soft Preopen Sets and Soft Pre Separation Axioms”. Gazi University Journal of Science 27, no. 4 (November 2014): 1077-83.
EndNote Akdağ M, Özkan A (November 1, 2014) On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science 27 4 1077–1083.
IEEE M. Akdağ and A. Özkan, “On Soft Preopen Sets and Soft Pre Separation Axioms”, Gazi University Journal of Science, vol. 27, no. 4, pp. 1077–1083, 2014.
ISNAD Akdağ, Metin - Özkan, Alkan. “On Soft Preopen Sets and Soft Pre Separation Axioms”. Gazi University Journal of Science 27/4 (November 2014), 1077-1083.
JAMA Akdağ M, Özkan A. On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science. 2014;27:1077–1083.
MLA Akdağ, Metin and Alkan Özkan. “On Soft Preopen Sets and Soft Pre Separation Axioms”. Gazi University Journal of Science, vol. 27, no. 4, 2014, pp. 1077-83.
Vancouver Akdağ M, Özkan A. On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science. 2014;27(4):1077-83.