Computable topological abelian groups Article Swipe

PDF

Related Concepts

abelian group mathematics locally compact space pure mathematics solenoid duality (order theory) pontryagin's minimum principle arithmetic function topological group topology (electrical circuits) discrete mathematics algebra over a field combinatorics physics mathematical optimization quantum mechanics optimal control

Martino Lupini , Alexander Melnikov , André Nies ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2105.12897 · OA: W4306710338

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.