On Functions Whose Graph is a Hamel basis

Krzysztof Plotka

We say that a function h: R --> R is a Hamel function if h, considered as a subset of R^2, is a Hamel basis for R^2. Shortly we write h \in HF. We prove that every function from R into R can be represented as a pointwise sum of two Hamel functions. The latter can be stated equivalently as the inequality A(HF) >= 3, where A(HF) is the smallest cardinality of a family F 'subset or equal'R^R for which there is no f \in R^R such that f + F 'subset or equal' HF.In addition we show that A(HF) <= \omega. 

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