We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.
@article{bwmeta1.element.bwnjournal-article-fmv146i3p203bwm,
author = {A. Ostrovsky},
title = {On open maps of Borel sets},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {203-213},
zbl = {0843.54039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i3p203bwm}
}
Ostrovsky, A. On open maps of Borel sets. Fundamenta Mathematicae, Tome 146 (1995) pp. 203-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i3p203bwm/
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