A fuzzy Pseudo-metric space is called fuzzy metric space iff it is sub-T0 space. Suppose that (X,F) is a fuzzy topological space. Consider a relation ~between ordinary points of X: x~y iff for each λ≠0,xλ∈yλ and yλ∈xλ. The relation~is an equivalent relation. The corresponding fuzzy quotien space is a sub-T0 space and is called the associated sub-T0 space of (X,F). in this paper, we establish the following theorem via fzzzy imbedding theory:Theorem Suppose that (X,F) is a fuzzy topological space with countable topological base. Then (1)(X,F) is fuzzy metrizable iff it is a fuzzy completely regular and sub-T0 space.(2)(X,F) is a fuzzy completely regular space,then its associated sub-T0 space is fuzzy metrizable. |