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Bad(r;s) is Hyperplane Absolute Winning
Abstract
Given an m-dimensional weight r and an n-dimensional weight s, we prove that the set of (r;s)-badly approximable m× n matrices is hyperplane absolute winning on ℝm× n. This fully answers a question \cite[Question 8.2 (iii)]{Kl} of D. Kleinbock in 1998.
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BibTeX
@misc{wu2026badrs,
title = {{$\mathbfBad(\mathbfr;\mathbfs)$ is Hyperplane Absolute Winning}},
author = {Chengyang Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22016},
eprint = {2609.22016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22016},
}
RIS
TY - UNPB
TI - Bad(r;s) is Hyperplane Absolute Winning
AU - Chengyang Wu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22016
UR - https://arxiv.org/abs/2609.22016
AB - Given an m-dimensional weight r and an n-dimensional weight s, we prove that the set of (r;s)-badly approximable m× n matrices is hyperplane absolute winning on ℝ^m× n. This fully answers a question \cite[Question 8.2 (iii)]{Kl} of D. Kleinbock in 1998.
ER -