The main result is slightly more general than the following statement: Let f: X → Y be a quasi-perfect mapping, where X is a regular space and Y a Hausdorff totally non-meagre space; if X or Y is χ-scattered, or if Y is a Lasnev space, then X is totally non-meagre. In particular, the product of a compact space X and a Hausdorff regular totally non-meagre space Y which is χ-scattered or a Lasnev space, is totally non-meagre.
@article{bwmeta1.element.bwnjournal-article-fmv153i2p191bwm,
author = {Ahmed Bouziad},
title = {Pr\'eimages d'espaces h\'er\'editairement de Baire},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {191-197},
zbl = {0895.54019},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p191bwm}
}
Bouziad, Ahmed. Préimages d’espaces héréditairement de Baire. Fundamenta Mathematicae, Tome 154 (1997) pp. 191-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p191bwm/
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