The following two theorems give the flavour of what will be proved. Theorem. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0,1] to Y coincide if and only if Y is connected and locally connected.Theorem. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class functions from [0,1] to Y coincide if and only if for all finite sequences of nonempty open subsets of Y there exists a continuous function ϕ:[0,1] → Y such that for all i ≤ q.
@article{bwmeta1.element.bwnjournal-article-fmv143i2p137bwm,
author = {M. Fosgerau},
title = {When are Borel functions Baire functions?},
journal = {Fundamenta Mathematicae},
volume = {142},
year = {1993},
pages = {137-152},
zbl = {0795.54039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i2p137bwm}
}
Fosgerau, M. When are Borel functions Baire functions?. Fundamenta Mathematicae, Tome 142 (1993) pp. 137-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i2p137bwm/
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