On defining soft spaces by weak soft neighborhood systems

Year 2016, Volume: 4 Issue: 2, 113 - 124, 01.03.2016

Taha Yasin Ozturk

Abstract

In the present paper, we define the concepts of weak soft neighborhood space, soft $w^{s}( \widetilde{\varphi },\widetilde{\varphi }^{^{\prime
}}) -continuous$, soft $w^{s}-continuous$ and soft $w^{s^{\ast }}-continuous$ on weak soft neighborhood spaces. Finally, we introduce their
basic properties and some examples.

Keywords

Weak soft neighborhood systems , weak soft neighborhood spaces

References

• Aktaş H. and Cağman N., Soft sets and soft group, Information Science 177 (2007) 2726-2735. Bayramov S., Gunduz (Aras) C. and Demirci N., A new approach to inverse and direct systems of soft topological spaces, Maejo International Journal of Science and Technology, 10(01) (2016) 51-65.
• Bayramov S. and Gunduz (Aras) C., Soft locally compact spaces and soft paracompact spaces, Journal of Mathematics and System Science, 3 (2013) 122-130.
• Csaszar A., Generalized topology, generalized continuity, Acta. Math. Hungar. 96 (2002) 351-357.
• Cağman N., Karatao S. and Enginoğlu S., Soft topology, Comput. Math. Appl. (2011) 351-358.
• Gunduz A. C., Sonmez A. and C¸ akallı H., On soft Mappings, (to appear).
• Maji P. K., Bismas R. and Roy A. R., Soft Set Theory, Comput. Math. Appl. 45 (2003) 555-562.
• Min W. K., On weak neighborhood systems and spaces, Acta. Math. Hungar. 121 (3) (2008) 283-292.
• Molodtsov D., Soft Set Theory-First Results, Comput. Math. Appl.37 (1999) 19-31.
• Ozturk T. Y. and Bayramov S., Soft mapping spaces, The Scientific World Journal, Article ID 307292, (2014) 8p.
• Shabir M. and Naz M., On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786-1799.
• Shabir M. and Bashir A., Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011) 4058-4067.
• Sahin R. and Küçük A., Soft Filters and Their Convergence Properties, Annals of Fuzzy Mathematics and Informatics 6(3) (2013) 529-543.
• Sahin R., Soft compactification of soft topological spaces: Soft star topological spaces, Annals of Fuzzy Mathematics and Informatics 10(2) (2015) 447-464.
• Thomas J. and John J. S., On soft generalized topological spaces, Journ. of New Results in Sci. 4 (2014) 01-15.