On defining soft spaces by weak soft neighborhood systems

On defining soft spaces by weak soft neighborhood systems

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 theirbasic properties and some examples.

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  • 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.