Isomorphism between Topological Groups.

Question

Let $G$ be an abelian profinite group and $G=\varprojlim G_i$ (all $G_i$ are finite).

Then why $\hom_{\text{cont}}(\varprojlim G_i,\mathbb{Q}/\mathbb{Z}) = \varinjlim\hom_{\text{cont}}(G_i,\mathbb{Q}/\mathbb{Z})$ as topological groups.