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Null Sets and Combinatorial Covering Properties by Szewczak, Piotr; Weiss, Tomasz is a scholarly article available to read on EtoBox.

What is Null Sets and Combinatorial Covering Properties about?

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 assumptions used in our constructions are far milder than used earlier by Galvin--Miller and Bartoszy\'nski--Rec{\l}aw, to obtain sets with analogous properties. We also consider products of Sierpi\'nski sets in the context of combinatorial covering properties.

Author

Szewczak, Piotr; Weiss, Tomasz

Published

2020

Language

EN