Products of perfectly meagre sets
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- by Ireneusz Recław PDF
- Proc. Amer. Math. Soc. 112 (1991), 1029-1031 Request permission
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.References
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N. Luzin, Ensembles de $I$-re catégorie, Fund. Math. 21 (1933), 114-126.
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- Wacław Sierpiński, Hypothèse du continu, Chelsea Publishing Co., New York, N. Y., 1956 (French). 2nd ed. MR 0090558 —, Sur un problème de M. Kuratowski concernant la propriété de Baire des ensembles, Fund. Math. 22 (1934), 262-266. E. Szpilrajn (Marczewski), Problème 68, Fund. Math. 25 (1935), 579.
Additional Information
- © Copyright 1991 American Mathematical Society
- 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