Préimages d’espaces héréditairement de Baire

Ahmed Bouziad

Fundamenta Mathematicae (1997)

  • Volume: 153, Issue: 2, page 191-197
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Bouziad, Ahmed. "Préimages d’espaces héréditairement de Baire." Fundamenta Mathematicae 153.2 (1997): 191-197. <http://eudml.org/doc/212221>.

@article{Bouziad1997,
author = {Bouziad, Ahmed},
journal = {Fundamenta Mathematicae},
keywords = {Baire space; totally non-meagre space; Lasnev space; χ-scattered space; quasi-perfect map; hereditary Baire; totally nonmeagre},
language = {fre},
number = {2},
pages = {191-197},
title = {Préimages d’espaces héréditairement de Baire},
url = {http://eudml.org/doc/212221},
volume = {153},
year = {1997},
}

TY - JOUR
AU - Bouziad, Ahmed
TI - Préimages d’espaces héréditairement de Baire
JO - Fundamenta Mathematicae
PY - 1997
VL - 153
IS - 2
SP - 191
EP - 197
LA - fre
KW - Baire space; totally non-meagre space; Lasnev space; χ-scattered space; quasi-perfect map; hereditary Baire; totally nonmeagre
UR - http://eudml.org/doc/212221
ER -

References

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  1. [AL] J. M. Aarts and D. J. Lutzer, The product of totally nonmeagre spaces, Proc. Amer. Math. Soc. 38 (1973), 198-200. Zbl0238.54028
  2. [D] G. Debs, Espaces héréditairement de Baire, Fund. Math. 129 (1988), 199-206. Zbl0656.54023
  3. [E] R. Engelking, General Topology, Heldermann, Berlin, 1989. 
  4. [G] G. Gruenhage, Generalized metric spaces, dans : Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), Elsevier, Amsterdam, 1984, 961-1043. 
  5. [H] W. Hurewicz, Relativ perfekte Teile von Punktmengen und Mengen (A), Fund. Math. 12 (1928), 78-109. Zbl54.0097.06

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