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2003-2004 Continuous images of big sets and additivity of $s_0$ under cpa$_{prism}$.
Krzysztof Ciesielski, Janusz Pawlikowski
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Real Anal. Exchange 29(2): 755-762 (2003-2004).


We prove that the Covering Property Axiom $CPA_{prism}, which holds in the iterated perfect set model, implies the following facts:

There exists a family $\mathcal{G}$ of uniformly continuous functions from $\mathbb{R}$ to $[0,1]$ such that $|\mathcal{G}|=\omega_1$ and for every $S\in[\mathbb{R}]^\mathfrak{c}$ there exists a $g\in\mathcal{G}$ with $g[S]=[0,1]$

The additivity of the Marczewski's ideal $s_0$ is equal to $\omega_1<\mathfrak{c}$.


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Krzysztof Ciesielski. Janusz Pawlikowski. "Continuous images of big sets and additivity of $s_0$ under cpa$_{prism}$.." Real Anal. Exchange 29 (2) 755 - 762, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1065.03028
MathSciNet: MR2083810

Primary: 03E35
Secondary: 03E17 , 26A03

Keywords: Additivity , continuous images , Marczewski's ideal $s_0$.

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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