On Functions Whose Graph is a Hamel Basis, II

http://dx.doi.org/10.4153/CMB-2009-032-x
Canad. Math. Bull. 52(2009), 295-302

  Published:2009-06-01
 Printed: Jun 2009

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 $\A(\ham)=\omega$.