Dini's Theorem

Theorem
Let $K \subseteq \R$ be compact.

Let $\left \langle {f_n} \right \rangle$ be a sequence of continuous real functions defined on $K$.

Let $\left \langle {f_n} \right \rangle$ converge pointwise to a continuous function $f$.

Suppose that:
 * $\forall x \in K : \left\langle{ f_n \left({ x }\right) }\right\rangle$ is monotone

Then the convergence of $\left \langle {f_n} \right \rangle$ to $f$ is uniform.