Markley characterized those
minimal sets arising from a homeomorphism of the circle without periodic points.
The removal of the condition that guarantees the space be metric yields a larger class
of minimal sets which can still be embedded in a circle-like object. A {long} {short}
circle is a compact connected {non-metric Hausdorff} {metric} space which has no
cut points, but which is disconnected by the removal of any two points. A circle is
either a long or short circle. Theorem: A compact Hausdorff minimal cascade can be
embedded in a homeomorphism of a circle without periodic points if and only if it is
proximally equicontinuous over the circle and P′⊆ Δ, where P is the proximal
relation.
