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On Local Quasi-Convexity as a Three-Space Property in Topological Abelian Groups

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URI: http://hdl.handle.net/2183/29915
DOI: 10.1016/j.jmaa.2021.125052

Publication date

2021

Authors

Tarieladze, Vaja

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Domínguez, X., Tarieladze, V. (2021). On local quasi-convexity as a three-space property in topological abelian groups. Journal of Mathematical Analysis and Applications, 499(2), 125052, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2021.125052. (https://www.sciencedirect.com/science/article/pii/S0022247X21001311)

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Abstract

[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, or if X is metrizable and H is a dually embedded subgroup which is also either discrete or bounded torsion. We also give some general principles and point out some errors we have found in the existing literature on this problem.

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Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG

Keywords

Locally quasi-convex group Three-space property Dually embedded subgroup Extension of topological abelian groups

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https://doi.org/10.1016/j.jmaa.2021.125052

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Atribución 4.0 Internacional

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Atribución 4.0 Internacional

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