On the existence of topologies compatible with a group duality with predetermined properties
Use este enlace para citar
http://hdl.handle.net/2183/35326
A non ser que se indique outra cousa, a licenza do ítem descríbese como Atribución-NoComercial-SinDerivadas 3.0 España
Coleccións
- GI-GMNE - Artigos [54]
Metadatos
Mostrar o rexistro completo do ítemTítulo
On the existence of topologies compatible with a group duality with predetermined propertiesData
2022Cita bibliográfica
Borsich, T., Domínguez, X., & Martín-Peinador, E. (2022). On the existence of topologies compatible with a group duality with predetermined properties. Topology and its Applications, 311, 107964. https://doi.org/10.1016/j.topol.2021.107964
Resumo
[Abstract:] 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 the dual pair (G, G∧) is equivalent to the semireflexivity in Pontryagin’s sense of the group G∧ endowed with the pointwise convergence topology σ(G∧, 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∧) is determined by a sort of completeness property of its Bohr topology σ(G, G∧) (Theorem 3.3).
Palabras chave
Group duality
Compatible topology
Equicontinuous subsets
k-group
kt-group
g-barrelled group
Pontryagin semireflexive group
Complete group
Compatible topology
Equicontinuous subsets
k-group
kt-group
g-barrelled group
Pontryagin semireflexive group
Complete group
Descrición
Versión aceptada de https://doi.org/10.1016/j.topol.2021.107964
Versión do editor
Dereitos
Atribución-NoComercial-SinDerivadas 3.0 España
Ítems relacionados
Mostrando ítems relacionados por Título, autor ou materia.
-
On Local Quasi-Convexity as a Three-Space Property in Topological Abelian Groups
Domínguez, Xabier; Tarieladze, Vaja (Elsevier, 2021)[Abstract] Let X be a topological abelian group and H a subgroup of X. We find conditions under which local quasi-convexity of both H and results in the same property for X. This is true for instance if H is precompact, ... -
Interest group influence in micro-states: the role of networking skills
Kanol, Direnç (Universidade da Coruña, Servizo de Publicacións, 2014)[Abstract] This paper argues that an interest group’s networking skills in micro-states may be as important, if not more important than other variables discussed in the interest group influence literature. This argument ... -
Topological Groups of Lipschitz Functions and Graev Metrics
Chasco, MJ; Domínguez, Xabier; Tkachenko, Mikhail (Elsevier, 2022)[Abstract] We study the properties of the free abelian topological group Ad(X) on a metric space (X,d) endowed with the topology generated by the Graev extension dˆ of a given metric d on X. We find that the group of ...