The concept of a fuzzy topology on a fuzzy set has been introduced in [1]. The aim of this work is to introduce fuzzy δ^*-continuity and fuzzy δ^**-continuity in this in new situation and to show the relationships between fuzzy continuous functions where we confine our study to some of their types such as, fuzzy δ-continuity, fuzzy continuity, after presenting the definition of a fuzzy topology on a fuzzy set and giving some properties related to it.