Plane separating continua inscribe rectangles

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.

13 pages