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 T1/2 – spaces .
A fuzzy topological spaces ( , ) is a fuzzy generalized regular spaces if ( , ) is fuzzy regular spaces and fuzzy T1/2 – 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 :
- ( , ) is a fuzzy semi s. regular spaces or fuzzy semi open regular spaces .
- 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).