The continuity of a function de ned between classical topological spaces is a fundamental_x000D_ and very important for the development of mathematics and its applications_x000D_ topological concept. However, due to the complexity of the real world and the imprecision_x000D_ contained in many phenomena of nature these are described or better_x000D_ explained by fuzzy sets , which were introduced by the engineer L. Zadeh (1965) [7]._x000D_ The concept of fuzzy set generalizes the classical notion of set . A fuzzy set A in_x000D_ a universe X is associated with a function A : X ! [0; 1] that assigns to each_x000D_ element x of X a real number A(x) in [0; 1] called \ degree of membership " of the_x000D_ element x to the set A. A higher degree of membership re_x000D_ ects a sense of belonging_x000D_ to \ more " strong set A._x000D_ This work is based on the theory of fuzzy topological spaces...