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Abstract

       In this study, we studied some of the different types of fuzzy regular spaces, included fuzzy semi closed regular spaces and fuzzy semi open  The standard distance, fuzzy semi s. regular, fuzzy generalized regular, fuzzy semi s. generalized  regular and we studied preservation theorems pertaining to these fuzzy spaces in addition to fuzzy hereditary includes that relate to these fuzzy spaces, and we reached to a few important results.

         The fuzzy topological spaces ( ,  ) is a fuzzy regular spaces and fuzzy semi – symmetric , then ( ,  ) is a fuzzy semi  T₂ – spaces .

A fuzzy topological spaces ( ,  ) is a fuzzy semi s. generalized  regular  spaces if and only if ( ,  )  is a fuzzy semi s. regular spaces and fuzzy semi  T_1/2 – spaces .

A fuzzy topological spaces ( ,  )  is a fuzzy generalized regular spaces if ( ,  )  is fuzzy regular spaces and fuzzy T_1/2 – spaces .

A fuzzy topological spaces ( ,  )  is a fuzzy generalized regular spaces if for every fuzzy open set   in , and (x)

Then there exist a fuzzy generalized open sets   such that (x) )^ᶢ(x)  (x).

Let ( ,  ) be a fuzzy topological spaces then the following statements are equivalent :

1. ( ,  ) is a fuzzy semi s. regular spaces or fuzzy semi open  regular spaces .
2. For fuzzy point  in  and for every fuzzy semi open set    contains  , there exist a fuzzy semi open set   such that (x) ^s(x))  (x) or (x) ^s(x))  (x).