Generalized oscillations for generalized continuities

Let (X, g) be a generalized topological space, (Y, d) a metric one and f : X → Y a function. We can define a generalized oscillation of f at x ∊ X as k^g_f (x) = inf{diamf(A) : A ∊ g, x ∊ A}. We discuss some properties of the generalized oscillation.