Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-2-4,
author = {Alexey Ostrovsky},
title = {Preservation of the Borel class under open-LC functions},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {191-195},
zbl = {1230.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-2-4}
}
Alexey Ostrovsky. Preservation of the Borel class under open-LC functions. Fundamenta Mathematicae, Tome 215 (2011) pp. 191-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-2-4/