Аннотация:
The notion of a weakly locally compact topological abelian group
introduced in this paper generalizes the notion of a fibrous
topological abelian group studied by N. Ya. Vilenkin.
Since in the class of locally compact topological abelian groups
we distinguish classes of compact and discrete topological
groups, in the class of weakly locally compact topological
abelian groups we distinguish classes of quasicompact and
quasidiscrete groups which are dual in the sense of Pontryagin's
theory of characters. We prove here that the group of characters
of a weakly locally compact topological abelian group is weakly
locally compact and construct universal groups for weakly
locally compact groups.
