  For a compactly generated LCA group $G$, it is shown that the set $H(G)$ of
all generalized characters on $G$ equipped with the compact-open topology is a
LCA group and $H(G) = \dg$ (the dual group of $G$) if and only if $G$ is
compact. Both results fail for arbitrary LCA groups. Further, if $G$ is second
countable, then the Gel'fand space of the commutative convolution algebra
$\ccg$ equipped with the inductive limit topology is topologically homeomorphic
to $\hg$.
