Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214246101