On functions whose graph is a Hamel basis

by

Krzysztof Plotka

10 pages; Proc. Amer. Math. Soc., to appear.

We say that a function h:R-->R is a Hamel function (h \in HF) if h, considered as a subset of R2, is a Hamel basis for R2. We prove that every function from R into R can be represented as a pointwise sum of two Hamel functions. The latter is equivalent to the statement: for all f1,f2:R-->R there is a g:R-->R such that g+f1 and g+f2 are in HF. We show that this fails for infinitely many functions.