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On Functions Whose Graph is a Hamel Basis, II
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- Journal:
- Canadian Mathematical Bulletin / Volume 52 / Issue 2 / 01 June 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 295-302
- Print publication:
- 01 June 2009
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- Article
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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 
$\text{A}\left( \text{HF} \right)\,=\,\omega$.
