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2010/2011 On the Lattice Generated by Hamel Functions
Grzegorz Matusik
Real Anal. Exchange 36(1): 65-78 (2010/2011).


We say that $f:\mathbb{R}\to \mathbb{R}$ is LIF if it is linearly independent over $\mathbb{Q}$ as a subset of $\mathbb{R}^2$ and that it is a Hamel function (HF) if it is a Hamel basis of $\mathbb{R}^2$. In this paper we present a discussion on the lattices generated by the classes HF and LIF. We also investigate extensions of partial LIF functions to HF and LIF functions defined on whole $\mathbb{R}


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Grzegorz Matusik. "On the Lattice Generated by Hamel Functions." Real Anal. Exchange 36 (1) 65 - 78, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1259.26002
MathSciNet: MR3016404

Primary: 15A03 , 54C40
Secondary: 26A21 , ‎54C30

Keywords: additive function , Hamel basis , Hamel function , lattice , linearly independent function

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
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