Hamel function

A function $h:{ℝ}^n\to ℝ$ is said to be a Hamel function if $h$, considered as a subset $\{(x,h(x)\}\subset {ℝ}^{n+1}$, is a Hamel basis for ${ℝ}^{n+1}$ over $\mathbb{Q}$. We denote the set of $n$-dimensional Hamel function by $HF({ℝ}^n)$.

References

• Poltka, K. On Functions Whose Graph is a Hamel Basis. Unpublised Ph.D. work. Online at http://academic.scranton.edu/faculty/PLOTKAK2/publications/ham_0911.pdf