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Let be an Abelian topological group.
A subgroup of is characterized
if there is a sequence
in the dual
group of such that
.
We reduce the study of characterized
subgroups of to the study of
characterized subgroups of compact
metrizable Abelian groups.
Let be the group of all
-valued null sequences and
be the uniform
topology on . If is compact
we prove that is a characterized
subgroup of if and only
if , where
and is a finite Abelian
group. For every compact Abelian...
It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups of an infinite Abelian group , for which there is an infinite subgroup of containing such that has a special decomposition into a direct sum which takes into account the properties of , and which induces a natural decomposition of into a direct sum of finite subgroups.
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