  We exhibit Pontryagin duality as a special case of Stone duality in a
continuous logic setting. More specifically, given an abelian topological group
$A$, and $\mathcal F$ the family (group) of continuous homomorphisms from $A$
to the circle group $\mathbb T$, then, viewing $(A,+)$ equipped with the
collection $\mathcal F$ as a continuous logic structure $M$, we show that the
local type space $S_\mathcal F(M)$ is precisely the Pontryagin dual of the
group $\mathcal F$ where the latter is considered as a discrete group.
  We conclude, using Pontryagin duality (between compact and discrete abelian
groups), that $S_\mathcal F(M)$ is the Bohr compactification of the topological
group $A$.
