An Example of a Quasi-continuous Hamel Function

Abstract

We say that $f: \mathR\to\mathR$ is a Hamel function if $f$, considered as a subset of $\mathR^2$, is a Hamel basis of $\mathR^2$. For a Cantor set $C\subset\mathR$ we construct a quasi-continuous Hamel function such that $f\restr(\mathR\setminus C)$ is of Baire class one.