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