Submission date: 24 April 2022

Abstract:

We exhibit Pontryagin duality as a special case of Stone duality in a continuous logic setting. That is, given an abelian topological group A, and F the family (group) of continuous homomorphisms from A to the circle group 𝕋, then viewing (A,+) equipped with the collection F, as a continuous logic structure M, the local type space S_F(M) is precisely the Pontryagin dual of the group F where the latter is considered as a discrete group. We conclude, using Pontryagin duality (between compact and discrete abelian groups) that S_F(M) is the Bohr compactification of the topological group A.

Mathematics Subject Classification:

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Full text arXiv 2204.11323: pdf, ps.