Atlas: On functions from R into R whose graph is a Hamel basis in R^2 by Krzysztof Plotka

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Boise Extravaganza in Set Theory
March 23-25, 2001
Boise State University
Boise, ID, USA

Organizers
Tomek Bartoszynski, Paul Corazza, Justin Moore

On functions from R into R whose graph is a Hamel basis in R^2
by
Krzysztof Plotka
West Virginia University

We say that a function h: R --> R is a Hamel function if h, considered as a subset of R², is a Hamel basis for R². 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) >= 2, 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.

Date received: March 9, 2001