Let $(X, \tau_X)$ and $(Y, \tau_Y)$ be topological spaces, and let $f: X \to Y$ be a function. Then $f$ is continuous if and only if for every net $(s_\alpha)_{\alpha \in D}$ in $X$ with $s_\alpha \to x$, the image net $(f(s_\alpha))_{\alpha \in D}$ converges to $f(x)$ in $Y$.