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arXiv · 2306.12445

Free group of Hamel functions

Mateusz Lichman·Michał Pawlikowski·Szymon Smolarek·Jarosław Swaczyna
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Abstract

We construct a free group of continuum many generators among those autobijections of $\mathbb{R}$ which are also Hamel bases of $\mathbb{R}^2$, 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 $\mathbb{R}^2$.

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Mateusz Lichman, Michał Pawlikowski, Szymon Smolarek, Jarosław Swaczyna. 2023-06-20. Free group of Hamel functions. https://arxiv.org/abs/2306.12445

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