English

Free group of Hamel functions

Group Theory 2023-06-23 v1

Abstract

We construct a free group of continuum many generators among those autobijections of R\mathbb{R} which are also Hamel bases of R2\mathbb{R}^2, with identity function included. We also observe two new cases when a real function is a composition of two real functions which are Hamel bases of R2\mathbb{R}^2.

Keywords

Cite

@article{arxiv.2306.12445,
  title  = {Free group of Hamel functions},
  author = {Mateusz Lichman and Michał Pawlikowski and Szymon Smolarek and Jarosław Swaczyna},
  journal= {arXiv preprint arXiv:2306.12445},
  year   = {2023}
}
R2 v1 2026-06-28T11:11:02.398Z