We study continuity points of functions with values in generalized metric spaces. We define the generalized oscillation, which is a useful tool in our study. Let X be a topological space and Y be a weakly developable space. Let ƒ
: X →Y be a function. Then the set C (ƒ) of continuity points of ƒis a Gδ-set in X. Some results concerning continuity points of separately continuous functions as well as functions with closed graphs are also given.