# 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}
}
• Published 18 June 2020
• Mathematics
• arXiv: General Topology
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…

## References

SHOWING 1-10 OF 30 REFERENCES
Products of Menger spaces: A combinatorial approach
• Mathematics
Ann. Pure Appl. Log.
• 2017
Combinatorial Cardinal Characteristics of the Continuum
The combinatorial study of subsets of the set N of natural numbers and of functions from N to N leads to numerous cardinal numbers, uncountable but no larger than the continuum. For example, how many
On Meager Additive and Null Additive Sets in the Cantor Space $2^{ω}$ and in ℝ
Let T be the standard Cantor–Lebesgue function that maps the Cantor space 2 onto the unit interval 〈0, 1〉. We prove within ZFC that for every X ⊆ 2, X is meager additive in 2 iff T (X) is meager
Linear $\sigma$-additivity and some applications
• Mathematics
• 2009
We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily σ-additive. Using this, together with infinite-combinatorial methods
SELECTIVE COVERING PROPERTIES OF PRODUCT SPACES, II: SPACES
• Mathematics
• 2015
We study productive properties of γ spaces, and their relation to other, classic and modern, selective covering properties. Among other things, we prove the following results: (1) Solving a problem
Selective covering properties of product spaces
• Mathematics
Ann. Pure Appl. Log.
• 2014