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Proceedings of the American Mathematical Society

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Products of perfectly meager sets and Lusin's function


Author: Janusz Pawlikowski
Journal: Proc. Amer. Math. Soc. 107 (1989), 811-815
MSC: Primary 54H05; Secondary 04A15
MathSciNet review: 984810
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Abstract: In [R] Recław solved an old problem of Marczewski by constructing two perfectly meager sets with a non-perfectly meager cartesian product. We show another method for getting such sets.


References [Enhancements On Off] (What's this?)

  • [K] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [L] N. Lusin, Sur les ensembles toujours de première catégorie, Fund. Math. 21 (1933), 114-126.
  • [Ma] E. Marczewski (Szpilrajn), Problem 68, Fund. Math. 24 (1935), 579.
  • [Mi] Arnold W. Miller, Special subsets of the real line, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 201–233. MR 776624
  • [R] I. Recław, Products of perfectly meager sets, preprint, 1987.
  • [S] W. Sierpiński, Hypothèse du continu, Chelsea, 1956.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0984810-3
Keywords: Perfectly meager, nowheredense, Lusin set
Article copyright: © Copyright 1989 American Mathematical Society