Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of topologies compatible with a group duality with
  predetermined properties   The paper deals with group dualities. A group duality is simply a pair $(G,
H)$ where $G$ is an abstract abelian group and $H$ a subgroup of characters
defined on $G$. A group topology $\tau$ defined on $G$ is {\it compatible} with
the group duality (also called dual pair) $(G, H)$ if $G$ equipped with $\tau$
has dual group $H$.
  A topological group $(G, \tau)$ gives rise to the natural duality $(G,
G^\wedge)$, where $G^\wedge$ stands for the group of continuous characters on
$G$. We prove that the existence of a $g$-barrelled topology on $G$ compatible
with the dual pair $(G, G^\wedge)$ is equivalent to the semireflexivity in
Pontryagin's sense of the group $G^\wedge$ endowed with the pointwise
convergence topology $\sigma(G^\wedge, G)$. We also deal with $k$-group
topologies. We prove that the existence of $k$-group topologies on $G$
compatible with the duality $(G, G^\wedge)$ is determined by a sort of
completeness property of its Bohr topology $\sigma (G, G^\wedge)$ (Theorem
3.3).

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg