Pontryagin dual

Summary

The Pontryagin dual of a locally compact abelian group $G$ is the group $\widehat{G}$ of continuous characters of $G$, with the compact-open topology. It is again a locally compact abelian group. The dual is the domain of the Fourier transform on $G$, and the Pontryagin duality theorem says that the dual of $\widehat{G}$ is $G$ again.