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PreprintCC BY-NC-SA 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{yaroshevskaya2026almost,
  title = {{Almost Periodic Characters and Hamel Coefficients in TVG Topologies on the Real Line}},
  author = {Irina Yaroshevskaya},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27633},
  eprint = {2610.27633},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27633},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Almost Periodic Characters and Hamel Coefficients in TVG Topologies on the Real Line
AU  - Irina Yaroshevskaya
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27633
UR  - https://arxiv.org/abs/2610.27633
AB  - 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.
ER  -