Some Mixed Soft Operations and Extremally Soft Disconnectedness via Two Soft Topologies

ABSTRACT

In this paper, we study the concept of soft sets which is introduced by
Molodtsov [5]. We give the definition of (τ_{1}，τ_{2})-semi open soft (resp. (τ_{1}，τ_{2})-pre open soft, (τ_{1}，τ_{2})-*α*-open soft, (τ_{1}，τ_{2})-*β*-open soft, (τ_{1}，τ_{2})＇-semi open soft, (τ_{1}，τ_{2})＇-pre open soft, (τ_{1}，τ_{2})＇-*α*-open soft, (τ_{1}，τ_{2})＇-*β*open soft) set via two soft topologies.
Also we introduce (τ_{1}，τ_{2})-regular open soft and *ESDC* on two soft topologies. The aim of this paper is to investigate
properties of some mixed soft operations and characterizations of *ESDC*. Finally, we study τ_{2}-*ESDC *soft topologies τ_{1}.

Cite this paper

N. Tas and A. Acikgoz, "Some Mixed Soft Operations and Extremally Soft Disconnectedness via Two Soft Topologies,"*Applied Mathematics*, Vol. 5 No. 3, 2014, pp. 490-500. doi: 10.4236/am.2014.53048.

N. Tas and A. Acikgoz, "Some Mixed Soft Operations and Extremally Soft Disconnectedness via Two Soft Topologies,"

References

[1] M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, “On Some New Operations in Soft Set Theory,” Computers & Mathematics with Applications, Vol. 57, No. 9, 2009, pp. 1547-1553.

http://dx.doi.org/10.1016/j.camwa.2008.11.009

[2] S. Hussain and B. Ahmad, “Some Properties of Soft Topological Space,” Computers & Mathematics with Applications, Vol. 62, No. 11, 2011, pp. 4058-4067.

http://dx.doi.org/10.1016/j.camwa.2011.09.051

[3] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-Latif, “γ-Operation and Decompositions of Some Forms of Soft Continuity in Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, 2014, to appear.

[4] P. K. Maji, R. Biswas and A. R. Roy, “Soft Set Theory,” Computers & Mathematics with Applications, Vol. 45, No. 4-5, 2003, pp. 555-562. http://dx.doi.org/10.1016/S0898-1221(03)00016-6

[5] D. Molodtsov, “Soft Set Theory—First Results,” Computers & Mathematics with Applications, Vol. 37, No. 4-5, 1999, pp. 19-31. http://dx.doi.org/10.1016/S0898-1221(99)00056-5

[6] M. Shabir and M. Naz, “On Soft Topological Spaces,” Computers & Mathematics with Applications, Vol. 61, No. 7, 2011, pp. 1786-1799. http://dx.doi.org/10.1016/j.camwa.2011.02.006

[7] I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, “Remarks on Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, Vol. 3, No. 2, 2012, pp. 171-185.

[1] M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, “On Some New Operations in Soft Set Theory,” Computers & Mathematics with Applications, Vol. 57, No. 9, 2009, pp. 1547-1553.

http://dx.doi.org/10.1016/j.camwa.2008.11.009

[2] S. Hussain and B. Ahmad, “Some Properties of Soft Topological Space,” Computers & Mathematics with Applications, Vol. 62, No. 11, 2011, pp. 4058-4067.

http://dx.doi.org/10.1016/j.camwa.2011.09.051

[3] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-Latif, “γ-Operation and Decompositions of Some Forms of Soft Continuity in Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, 2014, to appear.

[4] P. K. Maji, R. Biswas and A. R. Roy, “Soft Set Theory,” Computers & Mathematics with Applications, Vol. 45, No. 4-5, 2003, pp. 555-562. http://dx.doi.org/10.1016/S0898-1221(03)00016-6

[5] D. Molodtsov, “Soft Set Theory—First Results,” Computers & Mathematics with Applications, Vol. 37, No. 4-5, 1999, pp. 19-31. http://dx.doi.org/10.1016/S0898-1221(99)00056-5

[6] M. Shabir and M. Naz, “On Soft Topological Spaces,” Computers & Mathematics with Applications, Vol. 61, No. 7, 2011, pp. 1786-1799. http://dx.doi.org/10.1016/j.camwa.2011.02.006

[7] I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, “Remarks on Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, Vol. 3, No. 2, 2012, pp. 171-185.