Free group of Hamel bijections of big size
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909265618272256 |
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| author | Natkaniec, Tomasz |
| author_facet | Natkaniec, Tomasz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free group of Hamel bijections of big size Natkaniec, Tomasz Group Theory General Topology Primary: 20B99, Secondary: 03E35, 15A03, 26A18, 46A35 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. |
| title | Free group of Hamel bijections of big size |
| topic | Group Theory General Topology Primary: 20B99, Secondary: 03E35, 15A03, 26A18, 46A35 |
| url | https://arxiv.org/abs/2405.00952 |