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august 2015 Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions
Krzysztof Płotka
Bull. Belg. Math. Soc. Simon Stevin 22(3): 447-454 (august 2015). DOI: 10.36045/bbms/1442364591

Abstract

We prove the existence of an additive semigroup of cardinality $2^\mathfrak c$ contained in the intersection of the classes of Hamel functions ($\rm HF$) and Sierpiński-Zygmund functions ($\rm SZ$). In addition, we show that under certain set-theoretic assumptions the lineability of the class of Sierpiński-Zygmund functions ($\rm SZ$) is equal to the lineability of the class of almost continuous Sierpiński-Zygmund functions ($\rm AC\cap\rm SZ$).

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Krzysztof Płotka. "Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 447 - 454, august 2015. https://doi.org/10.36045/bbms/1442364591

Information

Published: august 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1350.26005
MathSciNet: MR3396995
Digital Object Identifier: 10.36045/bbms/1442364591

Subjects:
Primary: 15A03
Secondary: 03E75 , 26A21

Keywords: Hamel functions , lineability , Sierpiński-Zygmund functions

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 3 • august 2015
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