An example of a quasi-continuous Hamel function (Q416445)

The author shows that for every non-degenerate interval \(I\neq \mathbb R\) there exists a real-valued Hamel function such that \(f\!\upharpoonright \!I\) is in the first Baire class. Another result is the construction of a quasi-continuous real-valued Hamel function such that \(f\!\upharpoonright \!(\mathbb R \backslash C)\) is of Baire class one, where \( C\) is a Cantor set (i.e., it is homeomorphic to the ternary Cantor set). The author also poses two problems related with the obtained results.