Let $X, Y$ be topological spaces. Then a $f : X \rightarrow Y$ is said to be sequentially continuous if for every convergent sequence $x_n \rightarrow x$ in $X$ , $f(x_n) \rightarrow f(x)$ in $Y$ .

Every continuous function is sequentially continuous, however the converse is true only in first-countable spaces (for example in metric spaces).