Minimal subsystem
= Minimal subsystem
A <minimal subsystem> is a nonempty closed forward-invariant <subset> on which the restricted <dynamical system> is a <minimal dynamical system>. Every <continuous map> on a nonempty <compact Hausdorff space> has one: intersections of chains of nonempty closed invariant sets remain nonempty by <compactness>, so the <Zorn lemma> gives a minimal member.