Preservation of the Borel class under open-LC functions

Alexey Ostrovsky. "Preservation of the Borel class under open-LC functions." Fundamenta Mathematicae 213.2 (2011): 191-195. <http://eudml.org/doc/286484>.

@article{AlexeyOstrovsky2011,
abstract = {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.},
author = {Alexey Ostrovsky},
journal = {Fundamenta Mathematicae},
keywords = {Borel sets; locally closed sets; clopen sets; open and closed functions; Borel isomorphism},
language = {eng},
number = {2},
pages = {191-195},
title = {Preservation of the Borel class under open-LC functions},
url = {http://eudml.org/doc/286484},
volume = {213},
year = {2011},
}

TY - JOUR
AU - Alexey Ostrovsky
TI - Preservation of the Borel class under open-LC functions
JO - Fundamenta Mathematicae
PY - 2011
VL - 213
IS - 2
SP - 191
EP - 195
AB - 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.
LA - eng
KW - Borel sets; locally closed sets; clopen sets; open and closed functions; Borel isomorphism
UR - http://eudml.org/doc/286484
ER -