A New Perspective On Soft Topology

Abstract

In this paper, we approach the concept of soft topology with a different perspective. We define a soft topological space over given initial topological universe as a parameterization of subspaces of a topological space. In addition to this, we define some basic topological concepts such as Hausdorffness, compactness, connectedness for soft topological spaces and study their some properties. We give some results for relations between a topological space and a soft topological space that is defined on it.

Keywords

• Soft set,Soft topological space,Hausdorffness,Compactness,Connectedness

References

1. 1. Molodtsov, D. Soft set theory - first results. Comput. Math. Appl. 37 (1999) 19-31.
2. 2. Maji, PK, Biswas, R, Roy, AR. Soft set theory. Comput. Math. Appl. 45 (2003) 555-562.
3. 3. Ali, MI, Feng, F, Liu, X, Min, WK, Shabir, M. On some new operations in soft set theory. Comput. Math. Appl. 57 (2009) 1547-1553.
4. 4. Babitha, KV, Sunil, JJ. Soft set relations and functions. Comput. Math. Appl. 60 (2010) 1840-1849.
5. 5. Kim, YK, Min, WK. Full soft sets and full soft decision systems. J. Intell. Fuzzy Systems 26 (2) (2014) 925-933.
6. 6. Min, WK. Similarity in soft set theory. Appl. Math. Lett. 25 (3) (2012) 310- 314.
7. 7. Munkres, JR. Topology. 2nd, edition. Prentice Hall, Inc. 2000.
8. 8. Yuksel, Ş. General topology. 5th, extended edition. Eğitim Kitabevi Yayınları, 2006 (In Turkish).

9. 9. Shabir, M, Naz, M. On soft topological spaces. Comput. Math. Appl. 61 (7) (2011) 1786-1799.
10. 10. Aktaş, H, Çağman, N. Soft sets and soft groups. Inform. Sci. 177 (13) (2007) 2726-2735.
11. 11. Acar, U., Koyuncu, F., Tanay, B. Soft sets and soft rings. Comput. Math. Appl. 59(11)(2010) 3458-3463.