Real Analysis Exchange

Continuous images of big sets and additivity of $s_0$ under cpa$_{prism}$.

Krzysztof Ciesielski and Janusz Pawlikowski

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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 $\omega_1<\mathfrak{c}$.

Article information

Real Anal. Exchange, Volume 29, Number 2 (2003), 755-762.

First available in Project Euclid: 7 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results
Secondary: 03E17: Cardinal characteristics of the continuum 26A03: Foundations: limits and generalizations, elementary topology of the line

Continuous images additivity Marczewski's ideal $s_0$.


Ciesielski, Krzysztof; Pawlikowski, Janusz. Continuous images of big sets and additivity of $s_0$ under cpa$_{prism}$. Real Anal. Exchange 29 (2003), no. 2, 755--762.

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