Sequentially 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 sequentially continuous if $$ (\forall x \in X_1)(\forall {x_n}1^{\infty} \subset X_1) x_n \rightarrow{\tau_1} x \implies f(x_n) \rightarrow_{\tau_2} f(x) $$

Connection with topologically-continuous-function

If function is topologically-continuous-function then it is sequentially continuous.