PreprintarXiv licencearXiv
Plane separating continua inscribe rectangles
Abstract
We prove the following: If X is a plane separating continuum, then every embedding of X into ℝ2 contains the vertices of a Euclidean rectangle. We arrive to this result by extending a known result by H. Vaughan for Jordan curves to a wider class of topological objects via shape theory and Steenrod homology.
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BibTeX
@misc{moralesfuentes2026plane,
title = {{Plane separating continua inscribe rectangles}},
author = {Ulises Morales-Fuentes and Cristina Villanueva-Segovia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25574},
eprint = {2609.25574},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25574},
}
RIS
TY - UNPB
TI - Plane separating continua inscribe rectangles
AU - Ulises Morales-Fuentes
AU - Cristina Villanueva-Segovia
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.25574
UR - https://arxiv.org/abs/2609.25574
AB - We prove the following: If X is a plane separating continuum, then every embedding of X into ℝ^2 contains the vertices of a Euclidean rectangle. We arrive to this result by extending a known result by H. Vaughan for Jordan curves to a wider class of topological objects via shape theory and Steenrod homology.
ER -