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2005-2006 Additive Sierpiński-Zygmund functions.
Tomasz Natkaniec, Harvey Rosen
Author Affiliations +
Real Anal. Exchange 31(1): 253-270 (2005-2006).


In the paper we present an exhaustive discussion of the relations between Darboux-like functions within the class of additive Sierpiński-Zygmund (SZ) functions. In particular, we give an example of an additive Sierpiński-Zygmund (SZ) injection $f : \mathbb{R} \to\mathbb{R}$ such that $f^{-1}$ is not an SZ function. Under the assumption that $\mathbb{R}$ cannot be covered by less than $\mathfrak{c}$-many meager sets we give examples of an additive SZ bijection $f : \mathbb{R} \to\mathbb{R}$ such that $f^{-1}$ is not SZ and of an additive injection $f : \mathbb{R} \to\mathbb{R}$ such that both $f$ and $f^{-1}$ are SZ.


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Tomasz Natkaniec. Harvey Rosen. "Additive Sierpiński-Zygmund functions.." Real Anal. Exchange 31 (1) 253 - 270, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1110.26002
MathSciNet: MR2218841

Primary: 26A15
Secondary: 03E50

Keywords: additive function , almost continuous functions , CIVP-functions , connectivity functions , Darboux like function , functions with perfect road , peripherally continuous functions , SCIVP-functions , Sierpi{\'n}ski-Zygmund function

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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