Rectangle inscription for homogeneous planar continua

Determine whether every nondegenerate homogeneous planar continuum inscribes rectangles; equivalently, determine whether the pseudo-arc inscribes rectangles.

Background

The paper turns to non-separating plane continua and highlights the pseudo-arc as a central test case because it shares important properties with both the circle and the arc. It states that, by the classification of homogeneous planar continua, the question for all nondegenerate homogeneous planar continua is equivalent to the question for the pseudo-arc.

References

Does every non degenerate homogeneous planar continua inscribe rectangles? by the classification of homogeneous planar continua this is the same as asking if the pseudo-arc inscribes rectangles.

— Plane separating continua inscribe rectangles  (2609.25574 - Morales-Fuentes et al., 22 Sep 2026) in Section 4, Conclusions and further questions