AMApplied Mathematics2152-7385Scientific Research Publishing10.4236/am.2014.53048AM-42801ArticlesPhysics&Mathematics Some Mixed Soft Operations and Extremally Soft Disconnectedness via Two Soft Topologies ihalArabacıoğlu Tas1*AhuAcikgoz1*Department of Mathematics, Balikesir University, Balikesir, Turkey* E-mail:nihalarabacioglu@hotmail.com(IAT);ahuacikgoz@gmail.com(AA);070220140503490500October 23, 2013November 23, 2013 November 30, 2013© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

In this paper, we study the concept of soft sets which is introduced by Molodtsov [5]. We give the definition of (τ1，τ2)-semi open soft (resp. (τ1，τ2)-pre open soft, (τ1，τ2)-α-open soft, (τ1，τ2)-β-open soft, (τ1，τ2)＇-semi open soft, (τ1，τ2)＇-pre open soft, (τ1，τ2)＇-α-open soft, (τ1，τ2)＇-βopen soft) set via two soft topologies. Also we introduce (τ1，τ2)-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 τ2-ESDC soft topologies τ1.

(τ<sub>1</sub>，τ<sub>2</sub>)-Semi Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)-Pre Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)-<i>α</i>-Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)-<i>β</i>-Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)＇-Semi Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)＇-Pre Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)＇-<i>α</i>-Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)＇-<i>β</i>-Open Soft; (τ<sub>1</sub>，τ<sub>2</sub>)-Regular Open Soft; ESDCReferencesM. 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.2008.11.009S. 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.2011.09.051A. 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.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)00016-6D. 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)00056-5M. 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.2011.02.006I. 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.