In this work we continue  to investigate  the properties  of soft semi-open and soft semi-closed sets in soft topological spaces. We define a new type of soft semi-open and  soft semi-closed sets as stronger  forms of them,  named  SSc-open  and  SSc- closed sets.   The  class of SSc-open  sets is weaker than  the  class of soft regular closed sets.  Then  we introduce  the  concept  of SSc-neighbourhood,  SSc-derived, SSc-interior,  SSc-closure and SSc-boundary in soft topological spaces. It is shown that  if X  is soft extremally  disconnected  space, then  the family of SSc-open sets forms a soft topology on X  and whenever X  is soft locally indiscrete  space, then both the families of SSc-open sets and soft semi-open sets are identical.  It is shown that  every soft open set is an SSc-open  when X  is a soft regular  space.   Using this  set we define new types of soft mappings  called SSc-continuous  and  θSSc- continuous  mappings.    It  is shown that  SSc-continuity implies θSSc-continuity and SSc-continuity is stronger than  soft semi-continuity.  It is observed that  θSSc- continuity  is stronger  than  soft almost  semi-continuity.   Furthermore, some con- ditions are provided that  make SSc-continuity and θSSc-continuity equivalent to some other types of soft continuity.

Finally, some new types  of soft separation  axioms are defined and  investigated. The  axioms which separate  soft point are called SSc-Ti  spaces while the  axioms which separate  the ordinary point are called SSc-T ∗ spaces. It is proved that  SSc-Ti  (resp., SSc-T ∗) gives SSc-Ti−1  (resp., SSc-T ∗

) for (i = 1, 2) . It is shown that a soft space X  is SSc-T1  (resp.,  SSc-T ∗) if every soft point (resp.,  singleton soft set) is SSc-closed.  Also, it is shown that  SSc-Ti  and SSc-T ∗  spaces for (i = 0, 1) are independent except that  an SSc-T ∗ space implies SSc-T2  space.


[1] A. Acikgoz and N. A. Tas,  Some new soft sets and decompositions  of some soft continuities,  Annals  of Fuzzy Mathematics  and Informatics,  Vol. 9, No. 1, (2015), 23-35.

[2] M. Akdag and A. Ozkan,  Soft α-open  sets and soft α-continuous  functions, Abstract  and Applied Analysis, ID 891341,(2014), 1-7.

[3] M. Akdag and  A. Ozkan,  Soft b-open sets and  soft b-continuous  functions, Math. Sci., (2014) 8:124.

[4] N. Cagman  and  S. Enginoglu,  Soft set theory  and  uni-int  decision making, European  Journal  of Operational  Research,  Vol. 207, No. 2, (2010), 848-855.

[5] B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math. Inf. Sci., Vol. 7, No. 1, (2013), 287-294.

[6] B. Chen, Some local prpperties  of soft semi-open sets,  Discrete Dynamics in Nature  and Society, Vol. 2013, Article ID 298032, 6 pages.

[7] S. Das and  S. K. Samanta, Soft metric,  Annals  of Fuzzy Mathematics  and Informatics,  Vol. 6, No. 1, (2013), 77-94.

[8] I. Demir and O. B. Ozbakir, Soft Hausdorff spaces and their some properties, Annals of Fuzzy Mathematics  and Informatics,  Vol. 8, No. 5, (2014), 769-783.

[9] F. Feng, Y. B. Jun  and X. Zhao, Soft semirings, Computers  & Mathematics with Applications, 56 (2008), 2621-2628 .

[10] D. N. Georgiou, A. C. Megaritis  and V. I. Petropoulos,  On soft topological spaces, Appl. Math. Inf. Sci., Vol. 7, No. 5, (2013), 1889-1901.

[11] H. Hazra, P. Majumdar  and S. K. Samanta,  Soft Topology, Fuzzy Inf. Eng., 1, (2012), 105-115.

[12] R.  A. Hosny and  Deena  Al-Kadi,  Soft semi-open sets  with  respect  to  soft ideals, Applied Mathematics  sciences, Vol. 8, No. 150, (2014), 7487-7501.

[13] S. Hussain,  Properties  of soft semi-open  and  soft semi-closed sets,  Pensee Journal, 76(2)(2014), 133-143.

[14] G. Ilango and M. Ravindran, On soft preopen sets in soft topological spaces, Int.  Journal  Math. Research,  Vol. 5, No. 4, (2013), 399-409.

[15] K. Indirani and M. G. Smitha, On soft contra rgb-continuous function and soft almost  rgb-continuous  function  in soft topological spaces, Journal  of Global Research  in Mathematical  Archives , Vol. 2, No. 3, (2014), 60-73.

[16] 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 topo- logical spaces, Annals  of Fuzzy Mathematics  and  Informatics,  7(2),  (2014), 181-196.

[17] A. Kharal and B. Ahmad, Mappings of soft classes, New Math. Nat. Comput., 7, (2011), 471-481.

[18] D. V. Kovkov,  V. M. Kolbanov  and  D. Molodtsov,  Soft sets  theory-based optimization, Journal  of Computer  and Systems Sciences International, Vol. 46, No. 6, (2007), 872-880.

[19] J. Mahanta and P. K. Das, On soft topological space via semi open and semi closed soft sets, Kyungpook Math. J., 54(2014), 221-236.

[20] P. K. Maji, R. Biswas and R. Roy, Soft set theory, Computers & Mathematics with Applications, 45, (2003), 555-562.

[21] W.  K. Min,  A note  on soft topological  spaces,  Computers  & Mathematics with Applications, 62, (2011), 3524-3528.

[22] D. Molodtsov,  Soft set theory-first  results,  Computers  & Mathematics  with Applications, 37, (1999), 19-31.

[23] D. Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique  and its application,   Nechetkie Sistemy i Myagkie Vychisleniya,Vol. 1, No. 1, (2006), 8-39.

[24] D. Pei and  D. Miao, From  soft sets to information  systems,  Proceedings  of Granular Computing  IEEE,  International Conference,  Vol. 2, (2005),  617- 621.

[25] M. Shabir and M. Naz, On soft topological spaces, Computers & Mathematics with Applications, 61, (2011), 1786-1799.

[26] Z. Xiao, L. Chen, B. Zhong and S. Ye , Recognition for soft information based on the theory of soft sets, Annals of Fuzzy Mathematics  and Informatics,Vol. 6, No. 2, (2012), 425-431.

[27] S.Yuksel, Z. Guzel Ergul and N. Tozlu, Soft Regular Generalized Closed Sets in Soft Topological  Spaces,  Int.  Journal   of Math.  Analysis,  Vol. 8, No. 8, (2014), 355 – 367.

[28] Y. Yumak and A. K. kaymakci, Soft β-open sets and their applications,  J. of New Theory, 4(2015), 80-89.

[29] I. Zorlutuna  and H. Cakir, On Continuity of Soft Mappings, Appl Math. Inf. Sci., Vol. 9, No. 8, (2015), 403-409.

[30] I. Zorlutuna,  M. Akdag, W. K. Min and S. Atmaca,  Remarks  on soft topo- logical spaces, Annals  of Fuzzy Mathematics  and Informatics,  Vol. 3, No. 2, (2014), 171-185.