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On Functions Whose Graph Is a Hamel Basis
Proceedings of the American Mathematical Society
Vol. 131, No. 4 (Apr., 2003), pp. 1031-1041
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1194180
Page Count: 11
You can always find the topics here!Topics: Mathematical functions, Additivity, Cardinality, Mathematical sets, Continuous functions, Inductive definitions
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We say that a function h: R→ R is a "Hamel function" (h∈ 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,g+f2∈ HF. We show that this fails for infinitely many functions.
Proceedings of the American Mathematical Society © 2003 American Mathematical Society