Connected Subset of Union of Disjoint Open Sets

Theorem
Let $T = \struct{S, \tau}$ be a topological space.

Let $A$ be a connected subspace of $T$.

Let $U, V$ be disjoint open sets.

Let $A \subseteq U \cup V$.

Then
 * either $A \subseteq U$ or $A \subseteq V$.