论文标题
无效集合和组合覆盖属性
Null sets and combinatorial covering properties
论文作者
论文摘要
如果Cantor Cube的一个子集的子集为无效，则其代数和任何空集为NULL。我们构建了一组基数连续性，以至于：该集合中的所有连续图像均为无效，它包含一个并非无效的集合的同构副本，并且具有强大的组合覆盖属性的属性$γ$。我们还用属性$γ$构建了cantor Cube的非平凡子集，该子集并非无效。我们的构造中使用的设定理论假设要比Galvin-Miller和Bartoszyński-Recław的早期使用要远得多，以获得具有类似特性的集合。我们还考虑在组合覆盖属性的背景下进行Sierpiński集的产品。
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 $γ$, a strong combinatorial covering property. We also construct a nontrivial subset of the Cantor cube with the property $γ$ that is not null additive. Set-theoretic assumptions used in our constructions are far milder than used earlier by Galvin--Miller and Bartoszyński--Recław, to obtain sets with analogous properties. We also consider products of Sierpiński sets in the context of combinatorial covering properties.
