  Let $G$ be the group of all $\ZZ$-valued homomorphisms of the Baer-Specker
group $\ZZ^\NN$. The group $G$ is algebraically isomorphic to $\ZZ^{(\NN)}$,
the infinite direct sum of the group of integers, and equipped with the
topology of pointwise convergence on $\ZZ^\NN$, becomes a non reflexive
prodiscrete group. It was an open question to find its dual group $\hat{G}$.
Here, we answer this question by proving that $\hat{G}$ is topologically
isomorphic to $\ZZ^\NN\otimes_\mathcal{Q}\TT$, the (locally quasi-convex)
tensor product of $\ZZ^\NN$ and $\TT$. Furthermore, we investigate the
reflexivity properties of the groups of $C_p(X,\ZZ)$, the group of all
$\ZZ$-valued continuous functions on $X$ equipped with the pointwise
convergence topology, and $A_p(X)$, the free abelian group on a $0$-dimensional
space $X$ equipped with the topology $t_p(C(X,\ZZ))$ of pointwise convergence
topology on $C(X,\ZZ)$. In particular, we prove that $\hat{A_p(X)}\simeq
C_p(X,\ZZ)\otimes_\mathcal{Q}\TT$ and we establish the existence of
$0$-dimensional spaces $X$ such that $C_p(X,\ZZ)$ is Pontryagin reflexive.
