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arXiv · 2405.00952

Free group of Hamel bijections of big size

Tomasz Natkaniec
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Abstract

A $f\colon\mathbb{R}\to\mathbb{R}$ is called Hamel function if its graph is a Hamel basis of the linear space $\mathbb{R}^2$ over rationals. We construct, assuming CH, a free group of the size $2^\mathfrak{c}$ contained in the class of all Hamel functions, with the indentity function included. This answers, consistently, a question posed recently by M. Lichman, M. Pawlikowski, S. Smolarek, and J. Swaczyna.

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Tomasz Natkaniec. 2024-05-02. Free group of Hamel bijections of big size. https://arxiv.org/abs/2405.00952

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