Free group of Hamel functions
Volume 125 / 2023
Banach Center Publications 125 (2023), 91-98
MSC: Primary 20B99; Secondary 26A99, 54C40, 26A21.
DOI: 10.4064/bc125-8
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 the identity function included. We also find two new cases when a real function is a composition of two real functions which are Hamel bases of $\mathbb R^2$.
