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# On Functions Whose Graph is a Hamel Basis, II

Published:2009-06-01
Printed: Jun 2009
• Krzysztof P{\l}otka
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## Abstract

We say that a function $h \from \real \to \real$ is a Hamel function ($h \in \ham$) if $h$, considered as a subset of $\real^2$, is a Hamel basis for $\real^2$. We show that $\A(\ham)\geq\omega$, \emph{i.e.,} for every finite $F \subseteq \real^\real$ there exists $f\in\real^\real$ such that $f+F \subseteq \ham$. From the previous work of the author it then follows that $\A(\ham)=\omega$.
 Keywords: Hamel basis, additive, Hamel functions
 MSC Classifications: 26A21 - Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 54C40 - Algebraic properties of function spaces [See also 46J10] 15A03 - Vector spaces, linear dependence, rank 54C30 - Real-valued functions [See also 26-XX]