Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Yaroshevskaya, Irina
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223088562