Abstract
We introduce, for any topological abelian group G, the property of equicontinuity of arcs of \(G^\wedge _p\), the dual group of G endowed with its pointwise topology. We analyze the implications of this property, which we denote by EAP\(_\sigma \), and we present some representative examples. Furthermore we prove that if G satisfies EAP\(_\sigma \), every element of the arcwise connected component of \(G^\wedge _p\) can be written as \(\phi (1)\) for a suitable one-parameter subgroup \(\phi :\mathbb {R} \rightarrow G^\wedge _p\).
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Acknowledgements
The authors acknowledge the financial support of the Spanish AEI and FEDER UE funds. Grant: MTM2016-79422-P.
The authors also want to express their gratitude to Elena Martín Peinador and Tayomara Borsich for their feedback during the early stages of this project, and to the referee for his/her valuable suggestions.
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Chasco, M.J., Domínguez, X. (2019). Equicontinuity of Arcs in the Pointwise Dual of a Topological Abelian Group. In: Ferrando, J. (eds) Descriptive Topology and Functional Analysis II. TFA 2018. Springer Proceedings in Mathematics & Statistics, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-17376-0_4
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DOI: https://doi.org/10.1007/978-3-030-17376-0_4
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