NULL SETS AND COMBINATORIAL COVERING PROPERTIES

@article{Szewczak2020NULLSA,
  title={NULL SETS AND COMBINATORIAL COVERING PROPERTIES},
  author={Piotr Szewczak and Tomasz Weiss},
  journal={arXiv: General Topology},
  year={2020}
}
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set into the Cantor cube are null-additive, it contains a homeomorphic copy of a set that is not null-additive, and it has the property $\gamma$, a strong combinatorial covering property. We also construct a nontrivial subset of the Cantor cube with the property $\gamma$ that is not null additive. Set-theoretic… 

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