Non-separating indecomposable continua without rectangle inscription

Determine whether there exists a non-separating indecomposable plane continuum that does not inscribe rectangles, including whether the Knaster continuum inscribes rectangles.

Background

The paper’s main theorem handles plane separating continua, leaving the behavior of non-separating continua unresolved. This question asks whether indecomposability can coexist with failure of the rectangle-inscription property and identifies the Knaster continuum as a specific example.