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Duality of locally quasi-convex convergence groups

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Duality of locally quasi-convex convergence groups

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Sharma, P. (2021). Duality of locally quasi-convex convergence groups. Applied General Topology. 22(1):193-198. https://doi.org/10.4995/agt.2021.14585

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Título: Duality of locally quasi-convex convergence groups
Autor: Sharma, Pranav
Fecha difusión:
Resumen:
[EN] In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local ...[+]
Palabras clave: Continuous duality , Convergence groups , Local quasi-convexity , Pontryagin duality
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2021.14585
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2021.14585
Agradecimientos:
We thank Prof. H.-P. Butzmann and the anonymous reviewers for their many insightful comments and suggestions.
Tipo: Artículo

References

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R. Beattie and H.-P. Butzmann, Convergence Structures and Applications to Functional Analysis, Bücher, Springer Netherlands, 2013. [+]
L. Außenhofer, Contributions to the Duality Theory of Abelian Topological Groups and to the Theory of Nuclear Groups, Dissertationes mathematicae. Institute of Mathematics, Polish Academy of Sciences, 1999.

W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Matheatics, Springer Berlin Heidelberg, 1991. https://doi.org/10.1007/BFb0089147

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E. Martín-Peinador and V. Tarieladze, A property of Dunford-Pettis type in topological groups, Proc. Amer. Math. Soc. 132, no. 6 (2004), 1827-1837. https://doi.org/10.1090/S0002-9939-03-07249-6

P. Sharma, Locally quasi-convex convergence groups, Topology Appl. 285 (2020), 107384. https://doi.org/10.1016/j.topol.2020.107384

P. Sharma and S. Mishra, Duality in topological and convergence groups, Top. Proc., to appear.

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