Given a topological group $G$, I need to prove that
$\hat{G_1} \times \hat{G_2} \cong \widehat {G_1 \times G_2}$
where $\hat{G} = \{ \chi | \ \chi : G \rightarrow S^1 \}$ $ \ \ , $ ($\chi $ is a continuous group homomorphism and $S^1$ is the multiplicative group of all complex numbers of absolute value one). $\hat{G}$ itself is a topological group with the compact open topology.
Any help with this is appreciated!