Suppose $f: (X_1, d_1) \to (X_2, d_2)$ is a mapping of metric spaces. For any $\delta, \epsilon > 0$, let $$U_f^{\delta, \epsilon} = \{x \in X_1: \text{ there are }y, z \in B_{\epsilon}(x)\text{ with }d_2(f(y), f(z)) > \delta \}$$
How would use set operations with $U_f^{\delta, \epsilon}$ to obtain the points at which $f$ is continuous?