Abstract:

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.

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