On Weakly Measurable Functions

Volume 53 / 2005

Szymon Żeberski Bulletin Polish Acad. Sci. Math. 53 (2005), 421-428 MSC: 03E35, 03E75. DOI: 10.4064/ba53-4-7

Abstract

We show that if $T$ is an uncountable Polish space, $\mathcal{X}$ is a metrizable space and $f:T\rightarrow\mathcal{X}$ is a weakly Baire measurable function, then we can find a meagre set $M\subseteq T$ such that $f[T\setminus M]$ is a separable space. We also give an example showing that “metrizable” cannot be replaced by “normal”.

Authors

  • Szymon ŻeberskiInstitute of Mathematics
    University of Wroc/law
    Pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail

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