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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Products of perfectly meagre sets


Author: Ireneusz Recław
Journal: Proc. Amer. Math. Soc. 112 (1991), 1029-1031
MSC: Primary 28A05; Secondary 04A15
DOI: https://doi.org/10.1090/S0002-9939-1991-1059635-2
MathSciNet review: 1059635
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Abstract: We show that there exists a perfect set $ D \subseteq {2^\omega } \times {2^\omega }$ such that for every Luzin set in $ D$ both projections of it are perfectly meagre. It follows (under CH) that the product of two perfectly meagre sets need not be perfectly meagre (or even have the Baire property in the restricted sense). This provides an answer to a 55-year-old question of Marczewski.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1059635-2
Keywords: Perfectly meagre set, Luzin set
Article copyright: © Copyright 1991 American Mathematical Society