On a rectangle inclusion problem

Author:
Janusz Pawlikowski

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3189-3195

MSC:
Primary 03E05; Secondary 03E15, 54A35

DOI:
https://doi.org/10.1090/S0002-9939-1995-1264828-9

MathSciNet review:
1264828

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if every set of reals of size contains a meager-to-one continuous image of a set that cannot be covered by less than meager sets, then there exists a null (Lebesgue measure zero) subset of the plane that meets every nonnull rectangle . The antecedent is satisfied, e.g., if Cohen reals are added to a model of the continuum hypothesis.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1264828-9

Keywords:
Subsets of the plane,
nonnull rectangles,
closed null sets

Article copyright:
© Copyright 1995
American Mathematical Society