Topologically continuous function

Let $(X_1, \tau_1)$, $(X_1, \tau_2)$ - topological-space.

Function $f: (X_1, \tau_1) \rightarrow (X_2, \tau_2)$ considered topologically continuous if $$ (\forall x_1 \in X_1)(\forall V(f(x_1)) \in \tau_2): \exists U(x_1) \in \tau_1 \hookrightarrow f(U(x_1)) \subset V(f(x_1)) $$