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2008/2009 Darboux-like Functions within the Class of Hamel Functions
Krzysztof Płotka
Real Anal. Exchange 34(1): 115-126 (2008/2009).


In this paper we present a discussion of the relations of the classes of Darboux-like functions within the classes of Hamel functions and Sierpńiski-Zygmund Hamel functions. We prove that the inclusion relations among Darboux-like classes remain valid in both cases (under the assumption of CH for Sierpiński-Zygmund Hamel functions). In particular, assuming CH we prove the existence of a Sierpiński-Zygmund Hamel function which is connectivity but not almost continuous. In addition, we investigate the cardinal number Add $(F_1,F_2)$ in the case when one of the families $F_1,\; F_2$ is Darboux-like or Sierpiński-Zygmund and the other one is the class of Hamel functions, where Add $(F_1,F_2)$ is defined as the smallest cardinality of a family $F \subseteq \mathbb{R}^{\mathbb{R}}$ for which there is no $g \in F_1$ such that $g + F \subseteq F_2$


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Krzysztof Płotka. "Darboux-like Functions within the Class of Hamel Functions." Real Anal. Exchange 34 (1) 115 - 126, 2008/2009.


Published: 2008/2009
First available in Project Euclid: 19 May 2009

zbMATH: 05578218
MathSciNet: MR2527126

Primary: 26A15
Secondary: 03E50 , 03E75

Keywords: Darboux functions , Hamel functions , Sierpi:::'nski-Zygmund functions

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 1 • 2008/2009
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