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Search: MSC category 54C40 ( Algebraic properties of function spaces [See also 46J10] )

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1. CMB 2009 (vol 52 pp. 295)

P{\l}otka, Krzysztof
On Functions Whose Graph is a Hamel Basis, II
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
Categories:26A21, 54C40, 15A03, 54C30

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