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arXiv · 2609.25574

Plane separating continua inscribe rectangles

Ulises Morales-Fuentes·Cristina Villanueva-Segovia
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Abstract

We prove the following: If $X$ is a plane separating continuum, then every embedding of $X$ into $\mathbb{R}^2$ 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.

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Ulises Morales-Fuentes, Cristina Villanueva-Segovia. 2026-09-22. Plane separating continua inscribe rectangles. https://arxiv.org/abs/2609.25574

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