Suppose $f: E to N$ where $E$ is compact. The graph of $f$ is:

$$

G(f)={(x,f(x)):xin E}

$$

Also, assume that $G$ is compact.

Consider $(x_n) subseteq E, (x_n)to x$ and the corresponding sequence $(x_n,f(x_n)) subseteq G$. Since $G$ is compact, pick a subsequence:

$$

(x_{n_k},f(x_{n_k})) to (x,a)

$$

**Question:** Is $a=f(x)$?