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arXiv · 2610.27633

Almost Periodic Characters and Hamel Coefficients in TVG Topologies on the Real Line

Irina Yaroshevskaya
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Abstract

We study topological vector group topologies on the real line generated by Hamel coefficient functions and circle-valued characters. We determine their continuous characters, completions, and isomorphisms, and construct a sequence separating modular convergence from convergence of real-valued observations. We also classify precompact topologies and prove that no greatest nondiscrete topology exists. For the separate problem of a greatest compatible locally quasi-convex topology, we establish transfer and dilation criteria and rule out a family of dyadic counterexample constructions. The existence of a greatest compatible topology remains unresolved.

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Irina Yaroshevskaya. 2026-10-20. Almost Periodic Characters and Hamel Coefficients in TVG Topologies on the Real Line. https://arxiv.org/abs/2610.27633

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