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On a rectangle inclusion problem

Author: Janusz Pawlikowski
Journal: Proc. Amer. Math. Soc. 123 (1995), 3189-3195
MSC: Primary 03E05; Secondary 03E15, 54A35
MathSciNet review: 1264828
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Abstract: We show that if every set of reals of size $ {2^{{\aleph _0}}}$ contains a meager-to-one continuous image of a set that cannot be covered by less than $ {2^{{\aleph _0}}}$ meager sets, then there exists a null (Lebesgue measure zero) subset of the plane $ \mathbb{R} \times \mathbb{R}$ that meets every nonnull rectangle $ X \times Y$. The antecedent is satisfied, e.g., if $ {\omega _2}$ Cohen reals are added to a model of the continuum hypothesis.

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Keywords: Subsets of the plane, nonnull rectangles, closed null sets
Article copyright: © Copyright 1995 American Mathematical Society

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