Computable topological abelian groups [article]

Martino Lupini, Alexander Melnikov, Andre Nies
2021 arXiv   pre-print
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.
arXiv:2105.12897v2 fatcat:zgeiw3nxdrd2nhmam4qy5haj5e