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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 Hamel basis, additive, Hamel functions
MSC Classifications: 26A21, 54C40, 15A03, 54C30 show english descriptions Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]
Algebraic properties of function spaces [See also 46J10]
Vector spaces, linear dependence, rank
Real-valued functions [See also 26-XX]
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]
 

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