Definition:Sequential Continuity

Definition
Let $X$ and $Y$ be topological spaces, let $x \in X$.

Let $f : X \to Y$ be a mapping.

Then $f$ is said to be sequentially continuous at $x$ iff:


 * For every sequence $\left({x_n}\right)_{n \ge 1}$ in $X$ which converges to $x$, the sequence $\left({ f \left({x_n}\right) }\right)_{n \ge 1}$ converges to $f \left({x}\right)$ in $Y$.

Naturally, $f$ is said to be sequentially continuous iff it is sequentially continuous at every $x \in X$.