We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-7,
author = {Szymon \.Zeberski},
title = {On Weakly Measurable Functions},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {421-428},
zbl = {1102.03043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-7}
}
Szymon Żeberski. On Weakly Measurable Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 421-428. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-7/