论文标题
Cantor Cube中的错误识别
Error recognition in the Cantor cube
论文作者
论文摘要
基于T.〜Banakh，sz。〜GłąB，E.〜Jabłońska和J.〜Swaczyna最近引入的薄套件的概念，我们对无限的单人传输协议进行了研究。此类协议与一组可允许的消息相关联（即Cantor Cube $ \ Mathbb {Z} _2^ω$的子集。 使用Banach-Mazur游戏，我们证明所有检测到错误的协议都是Baire空间，而通用空间（尤其是最大）既不是Borel也不是微薄的。 我们还表明，可以将Cantor Cube分解为两个薄套件，这些套件可以被视为奇偶校验位的无限对应物。该结果与D.〜niwiński和E.〜Kopczyński在2014年定义的所谓XOR-SET有关。
Based on the notion of thin sets introduced recently by T.~Banakh, Sz.~Głąb, E.~Jabłońska and J.~Swaczyna we deliver a study of the infinite single-message transmission protocols. Such protocols are associated with a set of admissible messages (i.e. subsets of the Cantor cube $\mathbb{Z}_2^ω$). Using Banach-Mazur games we prove that all protocols detecting errors are Baire spaces and generic (in particular maximal) ones are not neither Borel nor meager. We also show that the Cantor cube can be decomposed to two thin sets which can be considered as the infinite counterpart of the parity bit. This result is related to so-called xor-sets defined by D.~Niwiński and E.~Kopczyński in 2014.
