Definition:Sequential Continuity
Jump to navigation
Jump to search
Definition
Let $X$ and $Y$ be topological spaces.
Let $f: X \to Y$ be a mapping.
At a Point
Let $x \in X$.
Then $f$ is sequentially continuous at $x$ iff:
- For every sequence $\left\langle{x_n}\right\rangle_{n \ge 1}$ in $X$ which converges to $x$, the sequence $\left\langle{f \left({x_n}\right)}\right\rangle_{n \ge 1}$ in $Y$ converges to $f \left({x}\right)$.
On a Domain
$f$ is sequentially continuous on $X$ iff $f$ is sequentially continuous at $x$ for every $x \in X$.