ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​​​​​​​​June 2018, Vol. 3, No. 6, pp 133-137. 

​​​Applications of Soft pre-open Sets to Soft W-Hausdorff Space in Soft Topological Spaces

A.M. Khattak¹,*, Z. A. Khattak², F. Jamal³, I. A. Khattak³, Z. U. Khattak⁴
¹Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan.
²Department of Mathematics, Bannu University of Sciences and Technology Bannu, Pakistan.
³Department of Mathematics, Qurtuba University of Science and Information Technology, Peshawar, Pakistan.
⁴Department of Mathematics, Hazara University, Mansehra, Pakistan.
​​*Corresponding author’s e-mail: mehdaniyal@gmail.com

Abstract

In the present article the notion of soft W-Hausdorf or soft W-T2 structure in soft topological spaces is proclaimed with respect to soft pre-open sets while using the ordinary points of Soft Topology. That’s why it is named as soft P-W-Hausdorf or soft P-W-T2 structure. Some sub-spaces of soft P-W- T2 structure are also reflected. Product of these spaces is also avail.

Keywords: Soft set; Soft P-open set; Soft P-closed set; Soft topological space; Soft P-W Hausdorf space.

References

  1. ​Molodstov D. Soft Set Theory – First Results. Computers and Mathematics with Applications. 37;1999:19-31.
  2. Shabir M, Naz M. On Soft Topological Spaces. Computers and Mathematics with Applications. 61;2011;1786-99.
  3. Khattak AM, Zaighum A, Khan GA, Ahmed I, Safer M, Khan S. Soft separation axioms in soft single point spaces and in soft ordinary spaces. Asian Journal of Mathematics and Computer Research. 2018;23(3):175-928.
  4. Naz M, Shabir M, Ali MI. Separation axiom in bi soft topological spaces. arXiv:1509.00866; 2015.
  5. Ittanagi BM. Soft bi-topological spaces, International Journal of Computer Application. 2014;107:1-4.
  6. El-Sheikh SA, Hosny RA, Abd-e-Latif AM. Characterization of b soft separation axioms in soft topological spaces. Inf Sci Lett. 2015;4:125-33.
  7. Khattak AM, Khan GA, Khan Y, Khattak MI, Jamal F. Characterization of Soft B-Separation Axioms in Soft Bi topological Spaces. Matrix Sains Matematik. 2018;2(2):11-17.
  8. Khattak AM, Younas M, Khan GA, RehmanMU, Nadeem S. P-Separation Axioms in Supra Soft Topological Spaces. Matrix Sains Matematik. 2018;2(2):7-10.
  9. Khattak AM, M Ishfaq, GA Khan, Z Anjum, Z Ullah, R Ullah, F Jamal. Soft Β W-Hausdorff Space in Soft Bi Topological Spaces, Matrix Sains Matematik. 2018;2(2):27-30.
  10. Maji PK, Riswas R, Roy AR. Soft Set Theory. Computers and Mathematics with Applications. 2003;45:555-62.
  11. Chang CL. Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications. 1968;24:182-190.
  12. Hussain S, Ahmad B. Soft separation axioms in soft topological spaces. Hacettepe Journal of Mathematics And Statistics. 2015;44:559-68.
  13. Arockiarani I, Lancy AA. Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces. International Journal of Mathematical Archive. 2013;4(2):1-7.
  14. Ali MI, Feng F, Liu X, Min WK, Shabir M. On some new operations in soft set theory. Computers and Mathematics with Applications. 2009;57:1547-53.
  15. Babitha KV, Sunil JJ. Soft set relations and functions. Comput Math Appl. 2010;60:1840-48.