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On Functions Whose Graph is a Hamel Basis, II

Published online by Cambridge University Press:  20 November 2018

Krzysztof Płotka
Krzysztof Płotka*
Affiliation:
Department of Mathematics, University of Scranton, Scranton, PA 18510, USA e-mail: Krzysztof.Plotka@scranton.edu
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Abstract

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We say that a function $h\,:\,\mathbb{R}\,\to \,\mathbb{R}$ is a Hamel function $(h\,\in \,\text{HF)}$ if $h$ , considered as a subset of ${{\mathbb{R}}^{2}},$ is a Hamel basis for ${{\mathbb{R}}^{2}}.$ We show that $\text{A}\left( \text{HF} \right)\,\ge \,\omega$ , i.e., for every finite $F\,\subseteq \,{{\mathbb{R}}^{\mathbb{R}}}$ there exists $f\,\in \,{{\mathbb{R}}^{\mathbb{R}}}$ such that $f\,+\,F\,\subseteq \,\text{HF}$ . From the previous work of the author it then follows that $\text{A}\left( \text{HF} \right)\,=\,\omega$ .

Keywords

26A2154C4015A0354C30Hamel basisadditiveand Hamel functions

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 295 - 302
Copyright
Copyright © Canadian Mathematical Society 2009

References

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