On extensions of fuzzy topologies

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A V (n A 6) | A, fi € T}. In tfys case we write T* = T(8). In this note we a t tempt to answer the general question: If (X, T) has property ' P ' under what conditions will (X, (T(S)) also have property ' P ' , where ' P ' is some fuzzy topological property.