Free group of Hamel functions

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 \(\m...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Lichman, Mateusz, Pawlikowski, Michał, Smolarek, Szymon, Swaczyna, Jarosław
Format: Article
Language:English
Online Access:Get full text
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Summary: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 \(\mathbb{R}^2\).
ISSN:2331-8422