  A subgroup $H$ of a topological abelian group $X$ is said to be characterized
by a sequence $\mathbf v =(v_n)$ of characters of $X$ if $H=\{x\in X:v_n(x)\to
0\ \text{in}\ \mathbb T\}$. We study the basic properties of characterized
subgroups in the general setting, extending results known in the compact case.
For a better description, we isolate various types of characterized subgroups.
Moreover, we introduce the relevant class of autochacaracterized groups
(namely, the groups that are characterized subgroups of themselves by means of
a sequence of non-null characters); in the case of locally compact abelian
groups, these are proved to be exactly the non-compact ones. As a by-product of
our results, we find a complete description of the characterized subgroups of
discrete abelian groups.
