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Addendum to “On Meager Additive and Null Additive Sets in the Cantor space $2^{\omega} $ and in $\mathbb R$” (Bull. Polish Acad. Sci. Math. 57 (2009), 91–99)

Volume 62 / 2014

Tomasz Weiss Bulletin Polish Acad. Sci. Math. 62 (2014), 1-9 MSC: 03E05, 03E15, 03E35. DOI: 10.4064/ba62-1-1


We prove in ZFC that there is a set $A\subseteq 2^{\omega}$ and a surjective function $H : A\to \langle0,1\rangle $ such that for every null additive set $X\subseteq \langle0,1)$, $H^{-1}(X)$ is null additive in $2^\omega$. This settles in the affirmative a question of T. Bartoszyński.


  • Tomasz WeissInstitute of Mathematics
    University of Natural Sciences and Humanities
    08-110 Siedlce, Poland
    Department of Mathematics
    Cardinal Stefan Wyszyński University in Warsaw
    Dewajtis 5
    01-815 Warszawa, Poland

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