Corpus ID: 235390586

On the existence of topologies compatible with a group duality with predetermined properties

@inproceedings{Borsich2021OnTE,
  title={On the existence of topologies compatible with a group duality with predetermined properties},
  author={T. Borsich and Xabier Dom'inguez and Elena Mart'in-Peinador},
  year={2021}
}
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 τ defined on G is compatible with the group duality (also called dual pair) (G,H) if G equipped with τ has dual group H. A topological group (G, τ) gives rise to the natural duality (G,G), where G stands for the group of continuous characters on G. We prove that the existence of a g-barrelled topology on G compatible with… Expand

References

SHOWING 1-10 OF 40 REFERENCES
Characteristics of the Mackey Topology for Abelian Topological Groups
This chapter is inspired on the Mackey-Arens Theorem, and consists on a thorough study of its validity in the class of locally quasi-convex abelian topological groups. If \(G\) is an abelian groupExpand
Abelian groups which satisfy Pontryagin duality need not respect compactness
Let G be a topological Abelian group with character group GA. We will say that G respects compactness if its original topology and the weakest topology that makes each element of GA continuousExpand
The Bohr compactification, modulo a metrizable subgroup
The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg (G): If G is a locally compact Abelian group with Bohr compact- ification bG, and if N is a closedExpand
$k$-groups and duality
Recall that a function is Ac-continuous if its restriction to each compact subset of its domain is continuous. We call a topological group G a Ac-group if each ¿-continuous homomorphism on G isExpand
On Mackey topology for groups
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensivelyExpand
Duality properties of bounded torsion topological abelian groups
Abstract Let G be a precompact, bounded torsion abelian group and G p ∧ its dual group endowed with the topology of pointwise convergence. We prove that if G is Baire (resp., pseudocompact), then allExpand
When a totally bounded group topology is the Bohr Topology of a LCA group.
We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a totally bounded abelian group $(G,w)$ is the Bohr reflection of a locallyExpand
Pontryagin duality for metrizable groups
Abstract. This paper deals with the validity of the Pontryagin duality theorem in the class of metrizable topological groups. We prove that completeness is a necessary condition for the PontryaginExpand
The Pontrjagin Duality Theorem in Linear Spaces
The Pontrjagin Duality Theorem, known to be true for locally compact groups, asserts that the given group and the character group of its character group are isomorphic under a "natural" mapping.Expand
Completeness properties of locally quasi-convex groups
It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be theExpand
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