<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <inline-formula id="j_aupcsm-2023-0006_eq_001"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2023-0006_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="M1"><mrow><msubsup><mi>ℤ</mi><mn>2</mn><mi>ω</mi></msubsup></mrow></math><tex-math><?CDATA \begin{eqnarray}{{\mathbb{Z}}}_{2}^{\omega }\end{eqnarray}?></tex-math></alternatives></inline-formula>).
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.
</abstract>

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 ℤ2ω).
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.

Error recognition in the Cantor cube

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Error recognition in the Cantor cube"}

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...

Error recognition in the Cantor cube

Online veröffentlicht: 12. Juli 2023

Seitenbereich: 75 - 86

Eingereicht: 17. Okt. 2022

Akzeptiert: 18. Mai 2023

DOI: https://doi.org/10.2478/aupcsm-2023-0006

© 2023 Paweł Pasteczka, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.