Computable topological abelian groups

Martino Lupini; Alexander Melnikov; Andre Nies

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arXiv · 2105.12897

Computable topological abelian groups

Martino Lupini·Alexander Melnikov·Andre Nies

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Abstract

We study the algorithmic content of Pontryagin - van Kampen duality. We prove that the dualization is computable in the important cases of compact and locally compact totally disconnected Polish abelian groups. The applications of our main results include solutions to questions of Kihara and Ng about presentations of connected Polish spaces, and an unexpected arithmetical characterisation of direct products of solenoid groups among all Polish groups.

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Martino Lupini, Alexander Melnikov, Andre Nies. 2021-05-27. Computable topological abelian groups. https://arxiv.org/abs/2105.12897

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