A note on soft topological spaces

Document Type : Research Paper

Authors

1 School of Mathematics and Statistics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China

2 School of Mathematics and Statistics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China

Abstract

This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the powerset lattice ($mathcal{P}(Xtimes E),subseteq$) of all subsets of $Xtimes E$. It therefore follows that soft topologies are redundant and unnecessarily complicated in theoretical sense.

Keywords

References

[1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010),
3458{3463.
[2] H. Aktas and N. C agan, Soft sets and soft groups, Inf. Sci., 177 (2007), 2726{2735.
[3] N. C agan, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011),
351{358.
[4] N. C agan and S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res.,
207 (2010), 848{855.
[5] B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math.
Inform. Sci., 7 (2013), 287{294.
[6] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621{2628.
[7] J. Gutierrez Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundan-
cies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intu-
itionistic fuzzy sets and topologies, Fuzzy Sets Syst., 156 (2005), 445{484.
[8] S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl.,
62 (2011), 4058{4067.
[9] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56 (2008), 1408{1413.
[10] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras,
Inf. Sci., 178 (2008), 2466{2475.
[11] P. K. Maji, R. Biswas and R. Roy, An application of soft sets in a decision making problem,
Comput. Math. Appl., 44 (2002), 1077{1083.
[12] P. K. Maji, R. Biswas and R. Roy, Soft set thoery, Comput. Math. Appl., 45 (2003), 555{562.
[13] W. K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011), 3524{3528.
[14] D. Molodtsov, Soft set theory rst results, Comput. Math. Appl., 37 (1999), 19{31.
[15] B. V. S. T. Sai and S. Kumar, On soft semi-open sets and soft semi-topology, Int. J. Math.
Arch., 4(4) (2013), 114-117.
[16] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786{
1799.
[17] F. G. Shi and B. Pang, Redundancy of fuzzy soft topological spaces, J. Intell. Fuzzy Syst., 27
(2014), 1757{1760.
Iranian Journal of Fuzzy Systems
Volume 12, Issue 5 - Serial Number 5
September and October 2015
Pages 149-155

Files

Share

How to cite

Statistics