A note on Soft Topology

Year 2016, Volume: 5 Issue: 11, 24 - 29, 25.08.2016

Jyothis Thomas Sunil Jacob John

https://izlik.org/JA67DJ94KA

Abstract

Cagman et al. (2011) [3] introduced soft topology on a soft set and deflned soft topological space. They deflned the basic notions of soft topological spaces such as soft open sets, soft closed sets, soft interior, soft closure, soft basis, soft neighborhood, soft limit point, soft boundary, soft subspace and soft Hausdorfi space and explored several basic properties of these concepts. But we found that some basic results are not true in general. The main purpose of this note is, with the help of counter examples, to establish that some results do not hold

Keywords

Soft sets , soft topology , soft open sets , soft closed sets , soft closure , soft limit point

References

• K. V. Babitha, J. J. Sunil, Soft set relations and functions, Computers and Mathematics with Applications, 60, 1840-1849, 2010.
• N. Cagman, S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207, 848-855, 2010.
• N. Cagman, S. Karatas, S. Enginoglu, Soft topology, Computers and Mathematics with Applications, 62, 351-358, 2011.
• P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45, 555-562, 2003.
• D. A. Molodtsov, soft set theory-flrst results, Computers and Mathematics with Applications, 37, 19-31, 1999.