PreprintarXiv licencearXiv
A bounded Borel set in the plane none of whose orthogonal projections is Borel
Abstract
We construct a bounded Borel set in the plane whose orthogonal projection onto every line is non-Borel. This gives a negative answer to a question of Thierry De Pauw.
Related
- Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions
- Prescribed projections for a general class of maps and efficient covering by variable plane curves
- A Bounded Finite-One Degree Whose One-One Degrees Form Exactly a Dense Linear Order
- Orthogonal Projections and Assouad Dimension: Resolving Fraser's Questions
- A new convergence proof for an iterative scheme for elliptic Cauchy problems based on alternating orthogonal projections
BibTeX
@misc{krokhalev2026bounded,
title = {{A bounded Borel set in the plane none of whose orthogonal projections is Borel}},
author = {Dmitrii Krokhalev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29809},
eprint = {2610.29809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29809},
}
RIS
TY - UNPB
TI - A bounded Borel set in the plane none of whose orthogonal projections is Borel
AU - Dmitrii Krokhalev
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29809
UR - https://arxiv.org/abs/2610.29809
AB - We construct a bounded Borel set in the plane whose orthogonal projection onto every line is non-Borel. This gives a negative answer to a question of Thierry De Pauw.
ER -