تقرير
Null sets and combinatorial covering properties
| العنوان: | Null sets and combinatorial covering properties |
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| المؤلفون: | Szewczak, Piotr, Weiss, Tomasz |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 37F20, 03E35, 03E75 |
| الوصف: | 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. Comment: 11 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1017/jsl.2021.51 |
| URL الوصول: | http://arxiv.org/abs/2006.10796 |
| رقم الأكسشن: | edsarx.2006.10796 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1017/jsl.2021.51 |
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